This paper presents a coordination scheme of automated vehicles at an intersection without using any traffic lights under a connected vehicles environment. Vehicles approaching the intersection from all sections are globally coordinated, by considering their states all together in a model predictive control framework, for their safe and rapid crossing. The optimal trajectories of the vehicles are computed based on avoidance of the cross-collision risks around the intersection. Compared with the other methods, the scheme enhances safety by generating the trajectories of vehicles far from each other with respect to the cross-collision points and enables turning movements under constrained velocity without using any auxiliary lanes. The proposed coordination scheme is evaluated through numerical simulation for a simple test intersection consisting of four single-lane approaches. Observations under different traffic flow conditions reveal that the proposed scheme significantly improves performance compared with the traditional traffic-light-based intersection control.