A symmetric matrix A ∈ ℝn×n is called copositive if it satisfies the inequality xT Ax ≥ 0 whenever x ≥ 0 and strictly copositive if xT Ax > 0, whenever 0 ≠ x ≥ 0. The ordering of a vector here is component-wise. Certain interesting properties of the inverse of a copositive matrix are extended to its Moore–Penrose inverse. The inheritance property of the Schur complement of a copositive matrix is extended to the case when the inverses in the Schur complement are replaced by their Moore–Penrose inverses. A framework is provided wherein one has the copositivity of B† - A†, given the copositivity of A-B. © 2016 Informa UK Limited, trading as Taylor & Francis Group.