Centroidal dynamics, which describes the overall linear and angular motion of a robot, is often used in locomotion generation and control of legged robots. However, the equation of centroidal dynamics contains nonlinear terms mainly caused by the robot's angular motion and needs to be linearized for deriving a linear model-predictive motion controller. This paper proposes a new linearization of the robot's centroidal dynamics. By expressing the angular motion with exponential coordinates, more linear terms are identified and retained than in the existing methods to reduce the loss from the model linearization. As a consequence, a model-predictive control (MPC) algorithm is derived and shows a good performance in tracking angular motions on a quadruped robot.