Decomposition of morphological structure element in hexagon lattice will be discussed in the paper by using the results proposed for decomposition in square lattice. Some important theoretical results on geometry of the decomposition, singularity, compatibility, and decomposability, etc. will be presented. Based on them, methodology for decomposition will be proposed, including approximate decomposition, correction of singularity, and so on. These results are general for all kinds of decompositions. As applications of the theory, several practical decomposing system in hexagon lattice, including 1D, points-pair, quasi 1D (points-pair), and that into neighborhood configurations will be analyzed theoretically, and efficient decomposing algorithms will be provided.