We propose a simple test for nontermination in the Knuth-Bendix completion algorithm. This test has the property that if there exists a simplification ordering that can generate a completion S of a set R of rules, then S may be generated from R using this test. Also, this test is user friendly in that it does not require any detailed knowledge of termination orderings. However, this technique may generate completions S that are not terminating; therefore, traditional methods for proving termination need to be used on the locally confluent sets S of rewrite rules that are obtained. We show that this test may be implemented in reasonable time and space bounds.