You can write a small Perl script in order to remove exact matches from a FASTA file. You can, for example, store all entries in hashes using the headers as keys and the sequences as values, that way you will clean your file. Just be careful with sequences that are exact in nucleotides/amino acids but have different headers, in that case this strategy might not be adequate if you need them.
Try the solutions these links provide. Simple scripts/tools you can download and use, and these are reliable. I have made use of a couple of these in the past.