The construction of a space partition in a cluttered environment allows for the creation of graph-based paths, establishing safe navigation corridors for agents. Then, it exploits them according to the available control degrees of freedom and dynamical constraints. Evaluating corridor safety relies on the distance between the path points and the nearest obstacles, influencing the real-time performance and robustness of navigation. This paper revisits the convex lifting method for space partition, emphasizing the generation and enlargement of safe corridors. The iterative enlargement algorithm pursues an increase in average corridor width while ensuring a monotonic increase in the minimum corridor width.