The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two-parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge—Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.