Preventing diagonal flow direction in ArcGIS Desktop

I would like to prevent diagonal flow direction/accumulation, as it leads to frequent "river shortcuts". As shown on the picture, instead of following the river in blue, because of the coarse raster resolution, a shortcut is created between the two diagonally adjacent cells (indicated by the red arrows). Here, the grey raster is the filled DEM.

Is there any option in either the flow direction or the flow accumulation function that satisfies this constraint?