There are few exact numerical solutions to which results from multigroup transfer matrix algorithms can be compared. Therefore, for isotropic elastic scattering in the center-of-mass system, exact numerical values have been calculated for Pl(μ), 0   l 20, the average Legendre coefficient of the scattered particle in the laboratory system. Both projectile and target masses are allowed to vary between 1 and 238 amu. It can be concluded that significant numerical uncertainties are possible in the calculation of the higher order transfer matrices.