We study the transition of the fissioning nucleus from the saddle to the scission point through a dynamical approach. It involves the numerical solution of the bi-dimensional time-dependent Schr¨odinger equation (TDSE) with time-dependent potential. The axially symmetric extremely deformed nuclear shapes are described by modified Cassini ovals. The Hamiltonian in cylindrical coordinates and z is discretized by using special finite difference approximations of the derivatives. The initial wave-functions for TDSE are the eigen-solutions of the stationary Schr¨odinger equation whose potential corresponds to the saddle point deformation. The TDSE is solved by a Crank-Nicolson method associated with transparent conditions at numerical boundaries. The time evolution is calculated until the neck connecting the primary fission fragments suddenly breaks. The numerical solutions have been used to evaluate relevant scission properties in the case of the fissioning nucleus 236U.