A new IAM approach based on properties of the generalized inertia tensor and its derivatives for the molecules with internal rotation which have symmetry isomorphic to C 3£ (M) has been developed. For solution the torsional-rotational Hamiltonian is divided into parts dependent and independent on the internal rotational coordinate r. The Hamiltonian for the r-independent part has been reduced according to properties of the inverse of the generalized inertia tensor (IGIT) and derived up to sixth order with the matrix elements calculated. The Hamiltonian contains 5, 15, and 35 terms in the second, fourth, and sixth orders respectively. From the 35 terms in the sixth order it is possible to select empirically only those making the most significant contribution to the energy. Two ways of including the r-dependent part of the Hamiltonian were proposed. The first approach is a conventional method employing a Watson-like reduction producing in total seven threefold terms in the second order of the angular momentum operators. The second way is analogous to the one used for reducing the r-independent part and also is based on properties of the r-independent terms of the IGIT. It produces in total eight threefold terms in the second order of the angular momentum operators. Fitting as well as predictive capabilities of the model were tested and compared with those of the Watson-like effective Hamiltonian. Overall improvement of performance over the effective Hamiltonian with a smaller number of the empirically chosen determinable parameters has been achieved. The distortion of a molecule caused by the internal rotation-rotation interactions acquires a clear meaning in terms of the fourth and sixth order expansion coefficients as the generalized centrifugal distortion.