It appears to be common practice to form a divergence free (hyperstatic) basis for polynomial stress fields in a 3D continuum by exploiting Maxwell or Morera stress functions, or forming a basis for the complete space of stress fields and then applying a reduction process. An alternative simpler procedure is proposed which directly constructs a hyperstatic basis by considering a pair of complementary subspaces. This basis can be used in the formation of hybrid equilibrium elements or wherever equilibrated stress fields are required.