The common search patterns for cooperative coverage search methods of multiple Unmanned Aerial Vehicles (UAVs) under unknown environment are zigzag and spiral patterns. Considering the constraints of the UAV's turning radius, the zigzag pattern needs to make turning out of the search area, which can result in longer total path lengths, while the spiral pattern may result in large number of turns, especially near the center of the area. Focusing on the shortcomings of these two patterns, we derived an improved search pattern based on the guarantee of area coverage and dynamic constraints of UAVs. The moments and positions of each UAV's turning were adjusted according to the corresponding rules. Theoretical analysis and simulation results show that, the improved method can not only work better than zigzag and spiral patterns, but also have good ability of formation reconstruction when partial sensors or UAVs are damaged.