  Second order supersymmetric approach is taken to the system describing motion
of a quantum particle in a potential endowed with position-dependent effective
mass. It is shown that the intertwining relations between second order partner
Hamiltonians may be exploited to obtain a simple shape-invariant condition.
Indeed a novel relation between potential and mass functions is derived, which
leads to a class of exactly solvable model. As an illustration of our
procedure, two examples are given for which one obtains whole spectra
algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like
or singular-oscillator-like spectra depending on the values of the
shape-invariant parameter.
