We use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1( fn) > 1 on the blowups of the projective n-space for all n ≥ 2 and more generally on the blowups of products of projective spaces. These fn, for n = 3 have positive entropy, and for n ≥ 4 seem to be the first examples of pseudo- automorphisms with d1( fn) > 1 (and of non-product type) on rational varieties of higher dimensions.
