An efficient supervisor synthesis method is proposed based on the constraint transformation, since enforcing a logic expression of linear constraints on Petri nets essentially involves finding admissible constraints. It consists of cooperative algorithms that are used to obtain the logic expression of constraints for any set of forbidden markings, to remove redundant constraints using the quantity information of constraints, to judge the existence of a permissive supervisor, to equivalently reduce multiple constraints into a single one using net structural properties, and to approach the admissible constraints from the original ones for ordinary Petri nets. These algorithms are derived from a series of theorems and lemmas presented to construct the theory of constraint transformation or reduction. In addition, the linear constraint, whose uncontrollable subnet is a forward-concurrent free net, can be equivalently transformed into an admissible linear constraint using this method.