A graph is said to be View the MathML source-prime if, whenever it is a subgraph of a nontrivial Cartesianproductgraph, it is a subgraph of one of the factors. A diagonalizedCartesianproduct is obtained from a Cartesianproductgraph by connecting two vertices of maximal distance by an additional edge. We show there that a diagonalizedproduct of View the MathML source-primegraphs is again View the MathML source-prime. Klavžar et al. [S. Klavžar, A. Lipovec, M. Petkovšek, On subgraphs of Cartesianproductgraphs, Discrete Math.