A concept of role is widely and significantly used to design and implement secure information systems. A role shows a job function in an enterprise. In a role-based access control (RBAC) model, a role is a set of access rights. A subject doing a job is assigned with a role showing the job. In addition, a subject can play multiple roles in an enterprise. In addition to keeping systems secure, objects have to be consistent in presence of multiple conflicting transactions. Traditional locking protocols and timestamp ordering (TO) schedulers are based on principles "first-comer-winner" and "timestamp order" to make multiple conflicting transactions serializable, respectively. Since a transaction is associated with a collection of roles, we discuss which collection of roles is more significant than others. We discuss a role ordering (RO) scheduler so that multiple conflicting transactions are serializable in the significant dominant relation of roles.