The effective potential of a non-Abelian supersymmetric theory with internal isospin symmetry is considered. In the one-loop approximation it is shown that the potential is finite without renormalization, and that where it is not zero, it is complex. In two loops, as in one loop, it is shown that the effective potential of the scalar fields alone vanishes identically. Implications of these results are discussed with reference to possible spontaneous symmetry breaking.