Due to their high mobility, cost-effectiveness and flexibility in deployment, Unmanned Aerial Vehicles (UAVs) have gained significant attention. However, it also brings significant challenges, especially in security transmission. This paper proposes a joint optimization approach for transmission power and trajectory management, aiming to maximize the minimum secure transmission rate in a UAV relay system. The Block Coordinate Descent (BCD) method decomposes the proposed problem into three sub-problems. By introducing slack variables and leveraging the properties of convex functions through Taylor series at their lower and upper bounds, the sub-problems are converted into equivalent convex optimization problems, which then be solved alternatively. The simulation outcomes reveal that the proposed approach effectively prevents eavesdropping by malicious UAVs, maximizes the minimum secure transmission rate, and consequently boosts the overall security of the UAV relay system.