The deviations of values on a cohort table can be defined as the total of period, age, and cohort effects. This study pays attention to the fact that the total variation (sum of squared deviations) consists of individual variations of the three factors' effects and covariation between them, and suggests decomposing the deviations into the three effects while maximizing the covariation. The maximization induces the behaviors of the three effects on the cohort table to be linked together as far as possible. The parts of the behaviors which are not capable of being linked are decomposable independent behaviors. The other parts which it is possible to link are considered as not decomposable linked behaviors. This study then shows that the estimated three factors' effects with this model are unbiased and reliable estimators. This model was applied to determine period, age, and cohort effects of 18 groups of food covered by The National Nutrition Survey in Japan.