We study the non-perturbative, instanton-corrected effective action of the N=2 SU(2)× SU(2) supersymmetric Yang–Mills theory with a massless hypermultiplet in the bifundamental representation. Starting from the appropriate hyperelliptic curve, we determine the periods and the exact holomorphic prepotential in a certain weak coupling expansion. We discuss the dependence of the solution on the parameter q= Λ 2 2/ Λ 1 2 and several other interesting properties.