Abstract: With regard to discrete phenomena in the uniqueness of the Cauchy problem, F. Treves [1] pointed out that the Canchy problemu(x, o) = ut (x, o) = o has non-trivial solutions if and only if p=l, 3, 5. ...... Wang Guangying andothers I21 studied the Cauchy problem and Gousat problem and proved that both have a unique solution if and only if p%i, 3, 5. ...... Continuing to use the methodreferred to in Note C2]> this paper studies the Cauchy problem of Treves equation where p = l, 3, 5 ...... , puts forward the proof of the theorem that with ample and necessaryconditions, there exists C" solution, and at the same time, gives a number of its concrete expressions.