my $dir = "directory";  #### no trailing "/"
opendir ( DH, $dir ) || die "Cannot open $dir: $!"; #### no "\n"

foreach my $file ( readdir DH) # Note: only name, not full path
{
   next unless $file =~ /\.fa$/;
   
   open (READ, '<', "$dir/$file") || die "Cannot open $dir/$file: $!";  

   while (my $line =<READ>)
   {
      if ($line =~ /^>/)
      {
         print $line;
      }
   } 
   close READ;   
} 

close (DH);