In this paper, we deal with arbitrary convex and concave rectilinear module packing using the Transitive Closure Graph (TCG) representation. The geometric meanings of modules are transparent to TCG and its induced operations, which makes TCG an ideal representation for floor-planning/ placement with arbitrary rectilinear modules. We first partition a rectilinear module into a set of submodules and then derive necessary and sufficient conditions of feasible TCG for the submodules. Unlike most previous works that process each submodule individually and thus need post processing to fix deformed rectilinear modules, our algorithm treats a set of submodules as a whole and thus not only can guarantee the feasibility of each perturbed solution but also can eliminate the need of the post processing on deformed modules, implying better solution quality and running time. Experimental results show that our TCG-based algorithm is capable of handling very complex instances; further, it is very efficient and results in better area utilization than previous work.