open (FNAMES, "<$Form{han}.txt") 
  or die "Cannot open $Form{han}.txt: $!\n";

while(<FNAMES>){ # for every line in the file.
  chomp; # remove trailing end of line character
  unlink $_ or die "Cannot unlink $_: $!\n";
}

close FNAMES; # close it before you unlink it.
unlink "$Form{han}.txt" 
  or die "Cannot unlink $Form{han}.txt: $!\n";

##</code><code>##

unlink "$Form{han}.txt" 
  or die "Cannot unlink $Form{han}.txt: $!\n";