In this paper the tunneling boundary condition is reexamined in terms of the Morse function. The use of this function permits one, on the one hand, to describe the shape of the singularity when topology change is allowed, and, on the other hand, to define, in the same situation, a slicing procedure which allows one to define the boundary of superspace so that the tunneling wave function of the Universe which results is defined unambiguously. \textcopyright{} 1995 The American Physical Society.