  The supersymmetric approach in the form of second order intertwining
relations is used to prove the exact solvability of two-dimensional Schrodinger
equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This
two-parametric model is not amenable to conventional separation of variables,
but it is completely integrable: the symmetry operator of fourth order in
momenta exists. All bound state energies are found explicitly, and all
corresponding wave functions are built analytically. By means of shape
invariance property, the result is extended to the hierarchy of Morse models
with arbitrary integer and half-integer values $a_k=-(k+1)/2.$
