The dependence of the bead mean squared displacement on the position of the bead along the chain backbone is considered within the lateral motion model for the dynamics of linear chain polymer melts. The bead position dependence has been ignored in the previous development of this theory. In the lateral motion model, the effective bead friction coefficient increases as the bead mean squared displacement increases, due to the greater interchain correlations that result because of the noncrossability of the chain backbones. In this work, a position dependent model is considered for this bead friction coefficient. The resulting equations of motion for the chain have the form of a generalized Rouse model with a position and time dependent bead friction coefficient. These equations are solved numerically. It is found that the time dependence of the center bead mean squared displacement has the same form as predicted by the simpler theory, in which the dependence of quantities on the position of the bead along the chain backbone is ignored. The scaling of the terminal time and the center of mass diffusion constant on chain length are also found to be unchanged by the inclusions of the bead position dependence of the friction coefficient. The mean squared displacement, averaged over all beads in the chain, shows a stronger time dependence than the same quantity for the center bead. The predictions are in excellent agreement with the results from previous numerical simulations.