As Laurent_R says, this is an excellent strategy. Have a look at the entry for $INPUT_RECORD_SEPARATOR (usually spelled just $/) in perlvar. For example:

#! perl
use strict;
use warnings;

my $target = 'kitten';
my $count  =  0;

$/ = ">Header\n";

{
    local $/ = ">Header\n";

    while (my $string = <DATA>)
    {
        $string =~ s/\n//g;
        print "string is '$string'\n";
        $count += () = $string =~ /\Q$target/g;
    }
}

print "The target string '$target' occurs $count times in the file\n";

__DATA__
>Header
sushikitten
ilovethekit
tensushithe
kittenisthe
>Header
sushikittAn
ilovethekit
tensushithe
kittBnisthe
[download]

Output:

23:11 >perl 1474_SoPW.pl
string is '>Header'
string is 'sushikittenilovethekittensushithekittenisthe>Header'
string is 'sushikittAnilovethekittensushithekittBnisthe'
The target string 'kitten' occurs 4 times in the file

23:11 >
[download]

Hope that helps,