Summary: We present a technique for constructing monotone, high resolution, multi-dimensional upwind fluctuation distribution schemes for the scalar advection equation. The method combines the second-order Lax-Wendroff scheme with upwind positive streamwise invariant scheme via a fluctuation redistribution step, which ensures monotonicity (and which is a generalization of the flux-corrected transport approach for fluctuation distribution schemes). Furthermore, we introduce the concept of distribution piont, which, when related to the equivalent equation for the scheme, leads to a ‘preferred direction’ for limiting procedure, and hence to a new distribution of fluctuation, which retains second-order accuracy from the Lax-Wendroff scheme, even when the solution contains turning points. Experimental comparisons show that the new method compares favourably in terms of speed, accuracy and robustness with other, similar, techniques.