Wash and trim zucchini and cut into slices 1/8 inch thick.
Reserve 8 walnut halves for garnish and coarsely chop the rest.
Melt butter in heavy saucepan, add zucchini, and saute, stirring gently and constantly until almost tender, 3 to 5 minutes.
Add chopped walnuts, salt and pepper to taste.
Cook gently, stirring until zucchini is crisply tender.
Garnish with the walnut halves.