  The main result of this article is that we show that from supersymmetry we
can generate new superintegrable Hamiltonians. We consider a particular case
with a third order integral and apply the Mielnik's construction in
supersymmetric quantum mechanics. We obtain a new superintegrable potential
separable in Cartesian coordinates with a quadratic and quintic integrals and
also one with a quadratic integral and an integral of order seven. We also
construct a superintegrable system written in terms of the fourth Painleve
transcendent with a quadratic integral and an integral of order seven.
