Assume that En is the ring of the C∞ function germs at 0∈ Rn,M is the unique maximal ideal in En. If f ∈M2 and its quadratic Hessain is non-degenerate, then f is isomorphic to its quadratic Hessain. This is famous Morse lemma. In this paper, We will discuss C funtion germs in two variables. The results show that (1) If f∈M3?Exy and its cubic Hessain is non-degenerate, then f is isomorphic to its cubic Hessain. (2) If f∈M4?Exy and its Hessain of degree 4 is non-degenerate,then f is isomorphic to its Hessain of degree 4.Obviously, this is a generalization of Morse lemma. |