We investigated the mechanism by which the length of exciton coherent domain in the linear array of pigments is determined. Correctly solving a generalized master equation with memory function obtained by the second-order perturbation of the intermolecular interaction, we obtained an empirical formula for the length of exciton coherent domain, abbreviated as coherence length. In the absence of inhomogeneity, this coherence length is expressed by a linear function of the ratio between the intermolecular coupling strength U and the destructing force gamma of a coherent bond. In the presence of inhomogeneity, the coherence length is expressed by a linear function of U/gamma only approximately, and its deviation becomes significant when the degree of inhomogeneity is larger than about 100 cm(-1). Applying this formula to the LH2 antenna complex of photosynthetic purple bacteria Rhodopseudomonas acidophila, we found that the coherence length of B850 is about 5 bacteriochlorophyll molecules in the absence of inhomogeneity and about 4 in the presence of inhomogeneity. The coherence length of B800 is less than 1.6, confirming that the excited state of B800 is almost localized at one bacteriochlorophyll molecule.