This paper presents a heuristic for the constrained two-dimensional cutting problem in which a guillotine divides a plate into rectangular pieces. The objective of the proposed heuristic is to maximize the pattern value (that is, the total value of the pieces produced from the plate) while observing the constraint that the number produced of a piece can not exceed the demand for that piece. The algorithm uses a simple recursion approach to consider a set of cutting patterns with specified geometric features, and uses a bound technique to discard unpromising branches. It can give solutions competitive with those of other heuristic algorithms. Its solutions to some benchmark instances are better than those currently reported in the literature.