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The main result of this article is that we show that from supersymmetry wecan generate new superintegrable Hamiltonians. We consider a particular casewith a third order integral and apply the Mielnik's construction insupersymmetric quantum mechanics. We obtain a new superintegrable potentialseparable in Cartesian coordinates with a quadratic and quintic integrals andalso one with a quadratic integral and an integral of order seven. We alsoconstruct a superintegrable system written in terms of the fourth Painlevetranscendent with a quadratic integral and an integral of order seven.

Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion