The purpose of this paper is searching for control Lyapunov-Morse functions (CLMF) using genetic programming (GP) for input-affine systems on general manifolds. The CLMF is an extended control Lyapunov function (CLF) to have multiple critical points. It is shown that a continuous global stabilizer is derived from a CLF for the system. A discontinuous global asymptotic stabilizer is obtained from a CLMF as well as CLF. However, there is no method constructing CLMF systematically. Then, we propose a method of searching for CLMF via GP to design the global asymptotic stabilizer.