In this nice paper the author extend recent work by P. Bayard [Calc. Var. Partial Differ. Equ. 18, No. 1, 1–30 (2003; Zbl 1043.53027)] on the Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. Among other results, the authors prove a maximum principle for the curvature of spacelike admissible solutions of the equation of prescribed scalar curvature in Minkowski space, and an interior curvature bound leading to the existence of locally smooth solutions in the case of spacelike affine boundary data.