  We augment the dimension of the Euclidean space by one and the Picard
iteration of a contraction by a simple iteration on the real line such that the
resulting iteration becomes monotone increasing and bounded with respect to the
order defined by the Lorentz cone of the augmented space. This provides a
different way of showing the convergence of the Picard iteration of a
contraction, exhibiting the strong relationship between the Banach fixed point
principle and the ordering structure of the Euclidean space ordered by the
Lorentz cone.
