How about:

#Include the newline in the delimiter...
$delimiter = "================================\n";

local($/) = $delimiter;
my $cnt=1;
while(<INPUT>){
  my $outfile = "> output_file_" . $cnt;
  open(OUT,$outfile)||die"Cannot open $outfile\n$!\n";
  print OUT;
  close(OUT);
  $cnt++;
}
[download]

Just a simple and dirty example of what I think you are asking for. I used an iterator for giving unique filenames. You may have other requirements. :-)

Mick