Create a cut on the underside of the branch approximately 12" away from the trunk. Saw about 1/3 of the way through the branch.
Move a few inches farther out on the branch and saw through until the branch cut breaks.
The step cut prevents ripping and leaves a stub.
Finish the cut by pruning the stub off just beyond the branch bark ridge and the branch collar. Do not cut into the trunk creating a flush cut.
The final cut should leave a minimal wound and clean area to heal.