We study the magnetoresistance, deltarho_{xx}(B)/rho_0, of a high-mobility 2D electron gas in the domain of magnetic fields, B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where deltarho_{xx}(B)/rho_0 is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the {em second order} in the interaction parameter, $lambda$, a {em linear} B-dependence, deltarho_{xx}(B)/rho_0sim lambda^2omega_c/E_F with {em temperature-independent} slope emerges in this domain of B (here omega_c and E_F are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is {em unrelated} to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B-dependence of the {em phase} of the impurity-induced Friedel oscillations.
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