The constant centrifugal potential approximation (CCPA) is generalized so as to be applicable to the reactions of rotationally excited reactants. The accurate calculations of reaction probabilities are required only for J less than or equal to /Omega(i)/(MAX)(less than or equal to j(i)), where J is the total angular momentum quantum number, j(i) represents the initial rotational state of a reactant diatomic molecule, ni is the z component of J in the body-fixed frame in the initial arrangement and /Omega(i)/(MAX) is the maximum of such /Omega(i)/’s that : give significant contributions to the reaction. The method is applied to the D + H-2(v(i) = 0,j(i)) reaction with use of the hyperspherical coordinates, and is proved to be useful by comparing the results with those, of the authors’ own accurate calculations. The reaction mechanisms are clarified with respect to the dependence on Omega(i) and j(i).