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This paper continues with the construction of the exact solution for parabolic coupled systems of the type ut=Auxx, A1u(0,t)+B1ux(0,t)=0, A2u(l,t)+B2ux(l,t)=0, 0<x<1, t>0, and u(x,0)=f(x), where A1, A2, B1, and B2 are arbitrary matrices for which the block matrix (A1B1A2B2) is nonsingular, and A is a positive stable matrix. Although this problem has been solved in the literature (Soler et al., 2013), in this work we are using completely new conditions.