No, you don't need a separate breeder tank to breed the fish, HOWEVER, if you want to raise a number of the fry, breeding them in a separate tank where the breeders are removed once the spawning has occurred is highly suggested. (All Tetras like to eat their eggs if they can get to them.) I used 5 or 7 1/2 gal tanks for breeding and just 10 gal tanks for the parents ( keeping the males and females in separate tanks. ) It's not a big deal to have a separate tank.
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Hope this helps.