Pontryagin's Minimum Principle is a way of solving hybrid powertrain optimal energy management. This paper presents an improvement of a classical implementation. The core of this improvement consists in relaxing the tolerance on some intermediate steps of the algorithm in order to reduce the number of iterations and thereby reducing the number of operations required to compute an optimal solution. The paper describes both a classical implementation of Pontryagin's Minimum Principle as well as the improved version. Numerical simulations are conducted on an academic example to demonstrate the benefits of the proposed approach.