Let M=[A a] be a matrix of order m×n, where A ∈ ℝ m×(n-1) and a ∈ ℝm is an m×1 vector. In this article, we derive a formula for the Moore-Penrose inverse of M * M and obtain sufficient conditions for its nonnegativity. The results presented here generalize the ones known earlier. © 2008 Springer Science+Business Media, LLC.