It has been argues that the natural notion of independence for conditional probability systems is weaker than sequential equilibrium's consistency condition. Kohlberg and Reny(1992) provide an attractive extra condition on a conditioal probability system thatimplies equivalence to consistency. We provide an alternative condition and argue that it is a natural implication of independence. condition also implies equivalence to consistency, and so is equivalent to Kohlberg and Reny's. However, the motivation and formulation of the condition are different, providing an additional viewpoint from which to understand consistency.