my $dir = "directory/";
opendir ( DH, $dir ) || die "Cannot open $dir: $!.\n";
foreach ( readdir DH) {
	if (/\.fa$/){
		my $file = $_;
		open (READ, "$file") || die "Cannot open $file: $!.\n";  # here's the problem
		while (<READ>){
			if ( /^>/){
				print $_;
			}
		} 
	} close (READ);
} close (DH);