An extended algorithm for generating a polynomial form-P[f_m(W)sinh(p_mW), g_n(W)cosh(P_nW)]--of the s-transfer matrix related to linear and stationary problems of heat transfer in one-dimensional multilayered slabs is developed to avoid the matrix multiplication algebra. This algorithm has no limit, not only to the number but also to the nature of layers, and should improve the computational efficiency of so-called wall response factors employed in building energy calculations.