[en] The equations of the adiabatic representation for a collision problem are rederived in a new and compact way and the kinematic nature of the long-range matrix elements which arise in this representation is shown explicitly. Next, the matrix transformation of the adiabatic representation is introduced which greatly simplifies its asymptotic form. Actually, the asymptotic values of matrix elements are effectively subtracted. The relation of this transformation with the translational factor operator is demonstrated. In the case of one-electron diatomic system the explicit form of matrices introducing asymptotically adapted adiabatic representation is found