The S-matrix calculations for the P-wave scattering process of pions on nucleons are carried out with the help of the ND method. According to the Balázs method the numerator function N is considered in the three-pole effective-range approximation. We choose one of the poles in the nucleon pole, where the residue is known. The remaining two residues (bi,i=1,2) are to be calculated. We use the following input values: the ρ-meson and pion-nucleon (3,3) isobar N* discontinuities and the high-energy contributions in the crossed channels, and the nucleon pole in the direct channel. The matching procedure is the usual one: The right-hand side of one of the determining equations for the effective-range parameters bi is analytically established by the projections of the invariant amplitudes with the aid of the fixed-s dispersion relations in a regular point sR in the unphysical region. Then the complete determining equations are obtained by comparing these projections and their derivatives, respectively, in the matching point sR. Having thus determined the parameters bi and the effective-range ND amplitude of the state J=32, I=12, we compute the scattering length a13 on the basis of the noncorrelated physical parameters (g2,m,WR33,μ). Its magnitude a13=-0.019 is in excellent agreement with the experimental value of Barnes et al.