#Maybe this what you mean????
open (F1, '<' ,$file1) or die "Cannot open file $file1 for reading\n";
open (F2, '<', $file2) or die "Cannot open file $file2 for reading\n";

##</code><code>##

while ( <F1>, <F2> )
{  
   # throw away a line from file F1 - never to be used
   # end the loop if there are no more lines in F2
   # set $_ to the next line from F2

   # <F1> plays no role here - it is a No-Operation: NoOp
}

##</code><code>##

while ( <F2> ) 
{
  # $_ is a line from $file2
}