  Recently, it was shown that half BPS Supergravity solution of theories with
SU(2$|$4) symmetry algebra is given uniformly by determining a single function
which obeys three dimensional continuous Toda equation. In this paper, we study
the scale invariant solution of Toda equation. Our motivation is that some
solutions of half BPS sector of IIB supergravity, as one excepts from the
fermion description of the theory, are scale invariant. By defining two
auxiliary functions we prove that such solutions of Toda equation obey cubic
algebraic equation. We obtain some simpl solutions of Toda equation specially,
we observe that the PP-wave solution can be written in this fashion.
