Oaxaca and Ransom (1999) show that a detailed decomposition of the coefficients effect is destined to suffer from an identification problem since the detailed coefficients effect attributed to a dummy variable is not invariant to the choice of reference groups. It turns out that the identification problem in the decomposition equation is a disguised identification problem of constant and dummy variables in a regression equation. This paper proposes a simple and natural remedy for this problem by utilizing “normalized” regressions which enable us to identify the constant and estimates of each dummy variable. The identification problem is automatically resolved once we obtain “normalized” regression equations for two comparison groups.