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Let n be a positive integer, F be a non-Archimedean locally compact field ofodd residue characteristic p and G be an inner form of GL(2n,F). This is agroup of the form GL(r,D) for a positive integer r and division F-algebra D ofreduced degree d such that rd=2n. Let K be a quadratic extension of F in thealgebra of matrices of size r with coefficients in D, and H be its centralizerin G. We study selfdual cuspidal representations of G and their distinction byH from the point of view of type theory. Given such a representation pi of G,we compute the value at 1/2 of the epsilon factor of the restriction of theLanglands parameter phi of pi to the Weil group of K, denoted e(K,phi). When Fhas characteristic 0, we deduce that pi is H-distinguished if and only if phiis symplectic and e(K,phi)=(-1)^r. This proves in this case a conjecture byPrasad and Takloo-Bighash.

Repr\'esentations cuspidales de GL(r,D) distingu\'ees par une involution int\'erieure