Improperly cutting a large limb from a tree can tear away a long strip of bark and wound the tree, as seen in the left picture in the diagram. This can be avoided by making the cut properly as described below.
Cut the remaining stub off (to prevent tearing the bark make a small cut at 'F' first) make the cut close to the main trunk.However, don't cut into the "branch collar" of the limb being removed, as this will actually inhibit healing. The branch collar is easily identified as the bulge between the base of the limb and the trunk.
Cut the limb from the underside about 1/2 way through but stop before the saw binds. This cut should be made at ‘A’ .