This paper presents a new algorithm to implement causal ordering. Causal ordering was first proposed in the ISIS system developed at Cornell University. The interest of causal ordering in a distributed system is that it is cheaper to realize than total ordering. The implementation of causal ordering proposed in this paper uses logical clocks of Mattern-Fidge (which define a partial order between events in a distributed system) and presents two advantages over the implementation in ISIS: (1) the information added to messages to ensure causal ordering is bounded by the number of sites in the system, and (2) no special protocol is needed to dispose of this added information when it has become useless. The implementation of ISIS presents however advantages in the case of site failures.