Kristian kindly sent me the newest version of bibtex4ht, which I attach
hereto. The date written in the file, March 2010, is incorrect. Also
with this version it did not work.

Now I installed Biblatex 0.9a instead of Biblatex 0.9d - and it works!
The result is not beautiful, but it went through.
Daniel

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% biblatex.4ht                          2010-03-31-15:16 %
% Copyright (C) 2007--2010       Eitan M. Gurari         %
%                                                        %
% This work may be distributed and/or modified under the %
% conditions of the LaTeX Project Public License, either %
% version 1.3c of this license or (at your option) any   %
% later version. The latest version of this license is   %
% in                                                     %
%   http://www.latex-project.org/lppl.txt                %
% and version 1.3c or later is part of all distributions %
% of LaTeX version 2005/12/01 or later.                  %
%                                                        %
% This work has the LPPL maintenance status "maintained".%
%                                                        %
% This Current Maintainer of this work                   %
% is the TeX4ht Project <[email protected]>.                %
%                                                        %
% If you modify this program your changing its signature %
% with a directive of the following form will be         %
% appreciated.                                           %
%            \message{signature}                         %
%                                                        %
%                                        [email protected]  %
%                             http://www.tug.org/tex4ht  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\immediate\write-1{version 2010-03-31-15:16}

   \ifx \...@startbib\:UnDef
      \pend:def\...@shorthands{%
   \pend:def\...@bibinit{%
       \HAssign\shorthands:cnt=0
       \NewConfigure{printfield-shorthand}{2}%
       \Configure{printfield-shorthand}%
         {\gHAdvance\shorthands:cnt by 1\relax
          \ifnum \shorthands:cnt=1 \a:printshorthands
          \else                    \c:printshorthands \fi
         }
         {\d:printshorthands}%
   \append:def\endtheshorthands{\b:printshorthands}%
   \csname a:@shorthands\endcsname
}}
\NewConfigure{printshorthands}{4}
\newconfigu...@shorthands}[1]{\concat:config\a:@shorthands{#1}}
\let\a:@shorthands\empty
\def\nolinkurl{\o:url:}
\def\...@checksum{\ifx \...@checksum@old \...@checksum@new \else
  \...@warning@noline {Page references have changed.\MessageBreak
    Rerun to get references righ...@tempswatrue \...@reruntrue \fi
  \...@nameuse {...@rerun}}
\pend:def\...@bibliography{%
  \pend:def\...@bibinit{%
     \ConfigureList{thebibliography}%
        {\a:thebibliography}%
        {\b:thebibliography}%
        {\c:thebibliography}%
        {\d:thebibliography}%
     \csname onthebibliography:list\endcsname
  }%
%  \pend:def\endthebibliography{%
%     \...@newlist \glob...@newlistfalse \fi
%  }%
}
\protected\def\...@finentry{%
  \unspace
  \a:finentry
      \finentrypunct
      \...@postpunct
  \b:finentry
  \...@initunit
}
\NewConfigure{finentry}{2}
\def\:tempc[#1]#2{%
   \expandafter\ifx \csname a:printfield-#2\endcsname\relax
      \NewConfigure{printfield-#2}{2}%
      \a:printfield{printfield-#2}%
   \fi
   \configure{...@unit}%
       {\csname a:printfield-#2\endcsname}%
       {\csname b:printfield-#2\endcsname}%
   \csname o:\string\...@printfield:\endcsname[#1]{#2}%
}
\expandafter\hlet\csname\string\...@printfield\endcsname\:tempc
\NewConfigure{printfield}[1]{\def\a:printfield##1{#1}}
\Configure{printfield}{%
    \Configure{#1}%
       {\HCode{<!--#1-->}}%
       {\HCode{<!--/#1-->}}%
}
\def\:tempc[#1]#2{%
   \expandafter\ifx \csname a:bibstring-#2\endcsname\relax
      \NewConfigure{bibstring-#2}{2}%
      \a:printfield{bibstring-#2}%
   \fi
   \configure{...@unit}%
       {\csname a:bibstring-#2\endcsname}%
       {\csname b:bibstring-#2\endcsname}%
   \csname o:\string\...@bibstring:\endcsname[#1]{#2}%
}
\expandafter\hlet\csname\string\...@bibstring\endcsname\:tempc
\def\:tempc[#1]#2{%
   \expandafter\ifx \csname a:bibcpstring-#2\endcsname\relax
      \NewConfigure{bibcpstring-#2}{2}%
      \a:printfield{bibcpstring-#2}%
   \fi
   \configure{...@unit}%
       {\csname a:bibcpstring-#2\endcsname}%
       {\csname b:bibcpstring-#2\endcsname}%
   \csname o:\string\...@bibcpstring:\endcsname[#1]{#2}%
}
\expandafter\hlet\csname\string\...@bibcpstring\endcsname\:tempc
\def\:tempc[#1]#2{%
   \expandafter\ifx \csname a:biblcstring-#2\endcsname\relax
      \NewConfigure{biblcstring-#2}{2}%
      \a:printfield{biblcstring-#2}%
   \fi
   \configure{...@unit}%
       {\csname a:biblcstring-#2\endcsname}%
       {\csname b:biblcstring-#2\endcsname}%
   \csname o:\string\...@biblcstring:\endcsname[#1]{#2}%
}
\expandafter\hlet\csname\string\...@biblcstring\endcsname\:tempc
\def\:tempc[#1]#2{%
   \expandafter\ifx \csname a:bibucstring-#2\endcsname\relax
      \NewConfigure{bibucstring-#2}{2}%
      \a:printfield{bibucstring-#2}%
   \fi
   \configure{...@unit}%
       {\csname a:bibucstring-#2\endcsname}%
       {\csname b:bibucstring-#2\endcsname}%
   \csname o:\string\...@bibucstring:\endcsname[#1]{#2}%
}
\expandafter\hlet\csname\string\...@bibucstring\endcsname\:tempc
\NewConfigure{biblatex-style}[2]{%
   \def\:temp{#1}%
   \ifx \:temp\...@cbxfile
      #2%
      \global\let\biblatex:style\def
   \fi
}
\pend:def\at:docend{%
   \ifx \UnDef\biblatex:style
      \:warning{\string\configure{biblatex-style}{\...@cbxfile}{...}
         not available}%
   \fi
}
\let\blx:it...@item
\d...@item[#1]{%
  \blx:item[#1]%
  \ifhmode \spacefactor\...@sf@par\fi
}
\let\...@resetpuncthook\@empty
\let\...@csq@ifkernma...@empty
\def\...@begunit{%
  \toggletrue{...@tempa}%
  \iftoggle{...@insert}%
    {\iftoggle{...@unit}%
       {\begingroup
          \let\...@begunit\@empty
          \let\...@endunit\@empty
          \...@unitpunct\blx@postpunct
        \endgroup
        \global\togglefalse{...@unit}%
        \togglefalse{...@tempa}}
       {\...@postpunct}%
     \iftoggle{...@block}%
       {\begingroup
          \let\...@begunit\@empty
          \let\...@endunit\@empty
          \newblockpunct
        \endgroup
        \global\togglefalse{...@block}%
        \togglefalse{...@tempa}}%
       {}}%
    {}%
  \...@postpunct
  \...@resetpuncthook
  \iftoggle{...@tempa}%
    {}%
    {\global\togglefalse{...@insert}}%
  \csname a:b...@unit\endcsname
  \...@leavevmode
  \...@csq@ifkernmark
    {}%
    {\penal...@m
     \hskip-\...@unitmark\relax
     \hskip\...@unitmark\relax}%
  \begingroup
    \configure{...@unit}{}{}%
}
\def\...@endunit{%
  \endgroup
  \csname b:b...@unit\endcsname
  \configure{...@unit}{}{}%
  \ifdim\lastskip=\...@unitmark
    \unskip\unskip\unpenalty
    \global\togglefalse{...@lastins}%
  \else
    \global\toggletrue{...@insert}%
    \global\toggletrue{...@lastins}%
  \fi
}
\newconfigure{...@unit}{2}

   \else
      
   \fi
   \NewConfigure{thebibliography}{4}
\append:def\...@bibinit{\a:bibinit}%
\NewConfigure{bibinit}{1}%

\def\...@field@entrykey{\thefield{entrykey}}

   \let\...@anchors\@empty
\protected\def\...@anchor{%
  \xifinlist{x\th...@refsection -%@
\...@field@entrykey}{\...@anchors}%
    {}%
    {\listxadd\...@anchors{x\the\c@refsection -%@
\...@field@entrykey}%
     \hyper:natanchorstart{x\th...@refsection -%@
\...@field@entrykey}%
     \hyper:natanchorend}}
\protected\def\...@bibhyperref{%
   \...@ifnextchar[%]
     {\...@bibhyperref@i}%
     {\...@bibhyperref@i[\...@field@entrykey]}}%
\long\def\...@bibhyperref@i[#1]#2{%
   \hyper:natlinkstart{x\th...@refsection -%@
#1}%
   #2\hyper:natlinkend}%
\protected\long\def\...@bibhyperlink#1#2{%
   \hyper:natlinkstart{x\th...@refsection --%:
#1}%
   #2\hyper:natlinkend}%
\protected\long\def\...@bibhypertarget#1#2{%
   \...@bsphack
   \hyper:natanchorstart{x\th...@refsection --%:
#1}%
   \...@esphack
   #2\hyper:natanchorend}%
\let\...@ifhyperref\@firstoftwo
\def\hyper:natanchorstart#1{\Link{}{#1}\EndLink}
\def\hyper:natanchorend{}
\def\hyper:natlinkstart#1{\Link{#1}{}}
\def\hyper:natlinkend{\EndLink}

   \let\:temp\do
  \def\do#1{%
    \patchcmd#1%
      {\co...@begingroup}%
      {\co...@begingroup\toggletrue{blx@footnote}}%
      {\togglefalse{...@tempa}\listbreak}%
      {}}%
  \docsvlist{%
    \...@footnotetext,%          latex
    \H@@footnotetext,%        hyperref
    \...@saved@footnotetext,% koma-script 3.x
    \...@dold@footnotetext,%    ledmac
    \...@doldold@footnotetext,% ledmac
    \...@fntori}%                frenchle
\let\do\:temp

\Hinput{biblatex}
\endinput


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