The dynamic model of a Four Control Moment Gyroscope (4-CMG) is traditionally obtained after computing the derivative of the angular momentum equation. Although this approach leads to a simple dynamic model, new models have been introduced due to terms not taken into account during the computation of the angular momentum equation. In this paper, a new dynamic model for a 4-CMG based on the Newton-Euler algorithm, which is well accepted in Robotics, was developed. This new approach produces a complete dynamic model.