Abstract: The estimation of flow direction is an important aspect in digital terrain analysis.There are two basic flow direction algorithms: the single flow direction algorithm (SFD) and the multiple flow direction algorithm (MFD).SFD only allows flow to follow in the steepest downslope direction and is not suited for modeling the dispersal flow over slope MFD allows flow to be distributed to all downhill neighbor cells.The currently three kinds of flow partition schemes are used by MFD algorithms: (1) weight ing the flow apportioning with constant exponent which will result in too diverging flow pattern; (2) using an accumulation based exponent which requires the accumulation distribution and an appropriate accumulation threshold determined mainly by using SFD or MFD; and (3) the "Form-based" MFD based on the analysis of the topographic form of a surface facet which is too sensitive to DEM's error.This paper presents a new MFD algorithm, MFD-fg.The basic idea of MFD-fg is that the flow partition scheme should spatially vary as the terrain changes so that the effect of the local terrain condition on the flow distribution can be reasonably modelled with the clear physical meanings.The experiments show that the linear function of the maximum downslope is an appropriate approach to measure the flow apportioning.Our experiment shows that the new approach, compared with SFD and other MFD approaches, get more reasonable flow accumulation index.