In [3] H. Steinhaus introduced the concept of a permutation function of the interval $[0,1)$ and proved several theorems about these functions. A. Mookhopadhyaya [2] and H. Miller [1] each have several results dealing with Steinhaus permutation functions. The purpose of this paper is to consider another class of functions, which we will call ``switch functions'', and show that they share certain properties with the Steinhaus permutation functions.