  The supersymmetric intertwining relations with second order supercharges
allow to investigate new two-dimensional model which is not amenable to
standard separation of variables. The corresponding potential being the
two-dimensional generalization of well known one-dimensional P\"oschl-Teller
model is proven to be exactly solvable for arbitrary integer value of parameter
$p:$ all its bound state energy eigenvalues are found analytically, and the
algorithm for analytical calculation of all wave functions is given. The shape
invariance of the model and its integrability are of essential importance to
obtain these results.
