In 1982, Fickett attempted to prove the Hyers-Ulam stability of isometries defined on a bounded subset of ${\mathbb{R}}^n$. In this paper, we applied an intuitive and efficient approach to prove the Hyers-Ulam stability of isometries defined on the bounded subset of ${\mathbb{R}}^4$, and we significantly improved Fickett's theorem for the four-dimensional case.