Moment-of-Fluid (MoF) is a piecewise linear interface reconstruction method that tracks fluid through its volume fraction and centroid, which are deduced from the zeroth and first moments. We present a method that replaces the original minimization stage by an analytic reconstruction algorithm on bi-dimensional Cartesian grids. This algorithm provides accurate results for a lower computational cost than the original minimization algorithm. When more than two fluids are involved, this algorithm can be used coupled with the minimization algorithm. Although this paper deals with Cartesian grids, everything remains valid for any meshes that are made of rectangular cells.