Preheat oven to 400 degrees.
Heat skillet over medium-high heat
Season both sides of salmon with salt and pepper liberally while skillet is heating
Melt butter in the skillet
Place fillets, skin side down, into skillet
Watch the sides of the steaks, and when half-done, move skillet into the oven
DO NOT MOVE SALMON once it is inside the skillet. If it sticks, it will unstick as it cooks.
Continue to bake until desired doneness, approximately 8-10 minutes, depending on its thickness.
For a well done salmon, cook up to 15 minutes
Use a meat thermometer and remove from oven when it reads 140+ degrees.
IF the salmon is a little dry, add another tablespoon butter to the skillet, then remove salmon and place on platter, skin side up.
Pour remaining butter from skillet over the top.
Serve.