Abstract: We classify normal forms of rigid hypersurfaces in C2 that are locally equivalent to a sphere, as closed form implicit equations in elementary functions. This result answers the long-standing question posed by N. Stanton in 1991 in the article where she obtained a partial list of rigid spherical hypersurfaces. It appears that Stanton's original list, is not complete (as she correctly conjectured) and has to be completed by a family that represents a solution of a system of non-linear PDE that is interesting in its own right.