Given an n -normed space with n ≥ 2 , we offer a simple way to derive an ( n − 1 ) -norm from the n -norm and realize that any n -normed space is an ( n − 1 ) -normed space. We also show that, in certain cases, the ( n − 1 ) -norm can be derived from the n -norm in such a way that the convergence and completeness in the n -norm is equivalent to those in the derived ( n − 1 ) -norm. Using this fact, we prove a fixed point theorem for some n -Banach spaces.