The purpose of this article is to prove the non-self multivariate contraction mapping principle in a Banach space. The main result is the following: let C be a nonempty closed convex subset of a Banach space (X, · ). Let T : C → X be a weakly inward N-variables non-self contraction mapping. Then T has a unique multivariate fixed point p ∈ C. That is, there exists a unique element p ∈ C such that T (p, p, · · · , p) = p. In order to get the non-self multivariate contraction mapping principle, the inward and weakly inward N-variables non-self mappings are defined. In addition, the meaning of N-variables non-self contraction mapping T : C → X is the following: