Conspicuous colouration in unpalatable organisms acts as a warning signal of their unprofitability, a phenomenon known as aposematism. The protection conferred by such colouration can lead to evolutionary convergence in warning signals between aposematic species, because sharing warning signals reduces the per capita cost of predator learning. Consequently, most aposematic species display a single colour pattern and participate in a single mimetic community (i.e. mimicry ring) at any given locality. However, some, like the Amazonian butterfly Heliconius numata, are polymorphic and participate in several mimicry rings within the same locality. We tested whether the unexpected polymorphism of H. numata could be due to a weak defence against predators. Poorly defended species participating in a mimicry ring are subject to negative frequency dependent selection, because their presence weakens the protection provided by the shared signal. This could promote polymorphism and participation in multiple mimicry rings. Using wild caught great tits (Parus major), we compared the palatability of H. numata to one of its locally monomorphic co-mimics (Mechanitis polymnia) and to two other locally monomorphic Heliconius species (H. melpomene and H. erato). The tested birds strongly rejected the polymorphic species H. numata, as well as the two other Heliconius species. Unexpectedly, a significantly weaker rejection was found towards M. polymnia, which relies on different toxic compounds to Heliconius. Our study demonstrates that the origin of polymorphic mimicry in H. numata is unlikely to stem from low unpalatability and raises new questions on defence variation within mimetic communities.