For square contingency tables with the same ordinal row and column classifications, McCullagh (1977) gave the marginal cumulative logistic model, which is an extension of the marginal homogeneity (MH) model using the logit transform. The present paper proposes a different extension of the MH model using the complementary log-log transform. In addition, the present paper gives the theorem that the MH model is equivalent to the proposed model and the equality of row and column marginal means holding simultaneously. In data analysis, if the MH model fits the data poorly, the theorem may be useful for seeing the reason for the poor fit. As example, the occupational status data for British father-son pairs are analyzed.