The switching times for the bang-bang control of linear time-invariant systems are investigated using the complex variable theory of entire functions. A general technique is presented which yields the switching times as the solution to a set of non-linear algebraic equations. Specific results are derived for three types of system transfer functions; (1) real poles—no zeros; (2) real poles and zeros; and (3) complex pole pair— no zeros. The complex pole case requires an algorithm to determine the number of switching times. The principal advantage of this approach is computational simplicity as compared to present iterative techniques.