  The cubic symmetry S_4 contains A_4 and S_3, both of which have been used to
study neutrino mass matrices. Using S_4 as the family symmetry of a complete
supersymmetric theory of leptons, it is shown how the requirement of breaking
S_4 at the seesaw scale without breaking supersymmetry enforces a special form
of the neutrino mass matrix which exhibits maximal nu_mu - nu_tau mixing as
well as zero U_e3. In addition, (nu_e + nu_mu + nu_tau)/sqrt{3} is naturally
close to being a mass eignestate, thus predicting tan^2 theta_12 to be near but
not equal to 1/2.
