Digital landforms maps, such as the excellent map published by the U.S. Geological Survey show clearly the old course of the Missouri.  The map below is adapted from the U.S.G.S.  maps.  The newer course, cutting across broken terrain, is not as clearindicating that it was formed quite recently,and has not been appreciably broadened by erosion on the sides.  The curved line drawn on the map is the southern limit of glaciation.  Compare the digital landforms map with the outline map showing the conjectured courses of the ancestors of the major rivers.
Notice on the landforms map that there are few deep river channels entering the Missouri across the rough upland between the Little Missouri River (just to the left of the (F)) and the Sheyenne River of South Dakota (running eastward from the Black Hills.  The Little Missouri used to run north, merge with the Yellowstone and meet the Missouri near the present U.S.-Canada boundary.  It therefore seems plausible that the uplift running through the Black Hills between the north-flowing rivers and the east-flowing rivers might at one time have formed the continental divide.  If that supposition is correct, the Missouri-Saskatchewan system may have drained to the north as shown on the outline map.  The outline map shows the ancestral Red River and James River flowing south; it is quite possible that they too at one time flowed northward.  These are my deductions; others believe that the Missouri Saskatchewan drained to the south, through either the James River depression or the Red River depression.  Of course both alternatives might have been correct at different times; There have been many advances of the ice age glaciers, and each time they thoroughly mixed up the river systems.
The map below shows