Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, we minimize a cost function with respect to the switching times. In this paper we propose an efficient method for computing optimal switching times in switched linear systems. We derive simple expressions for the cost function, the gradient and the Hessian which can be computed efficiently online without performing any integration. With the proposed method, the most expensive computations are decomposed into independent scalar exponentials which can be efficiently computed and parallelized. Simulation results show that our method is able to provide fast convergence and handle efficiently a high number switching times.