Unsignalized intersection cooperation of connected and automated vehicles (CAVs) is able to eliminate green time loss of signalized intersections and improve traffic efficiency. Most of the existing research on unsignalized intersection cooperation considers fixed lane direction, where only specific turning behavior of vehicles is allowed on each lane. Given that traffic volume and the proportion of vehicles with different turning expectation may change with time, fixed lane direction may lead to inefficiency at intersections. This paper proposes a multi-lane unsignalized intersection cooperation method that considers flexible lane direction. The two-dimensional distribution of vehicles is calculated and vehicles that are not in conflict are scheduled to pass the intersection simultaneously. The formation reconfiguration method is utilized to achieve collision-free longitudinal and lateral position adjustment of vehicles. Simulations are conducted at different input traffic volumes and turning proportion of incoming vehicles, and the results indicate that our method outperformances the fixed-lane-direction unsignalized cooperation method and the signalized method.