A simple finite difference scheme is used to solve the second order, simultaneous, non-linear partial differential equations with a nonhomogeneous boundary condition, to study the influence of a step discontinuity in the surface temperature on heat transfer from a vertical porous plate in free convection with uniform transpiration. The numerical procedure is described in detail and results are presented for Pr =0.72 in the blowing parameter range, - 1.5 < ©1< 1.5, for non-dimensional temperature range of 0.25 to 2.0. When the downstream section is cooler than the upstream section, an equilibrium point is defined, which moves towards the discontinuity on suction and away from it on blowing. The readjustment of the boundary layer is slow, causing the "recovery length" to be considerable. © 1986 Springer-Verlag.