Define 'big'. One way to handle the problem for smaller values of 'big' is to read the entire file into memory then use a regular expression to cut it up for you.

For larger values of big you may be able to use something like:

use strict;
use warnings;

local $/ = ">Seq";

while (<DATA>) {
    chomp;
    next if ! length;
    print "Record: $_\n";
}

__DATA__
>Seq1
AAATTTGGG.....
>Seq2
AGATTTACC.....
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