It is well-known that there are polysemous words like sentence whose "meaning " or "sense " depends on the context of use. We have recently reported on two new word-sense disambiguation systems, one trained on bilingual material (the Canadian Hansards) and the other trained on monolingual material (Roget's Thesaurus and Grolier's Encyclopedia). As this work was nearing completion, we observed a very strong discourse effect. That is, if a polysemous word such as sentence appears two or more times in a well-written discourse, it is extremely likely that they will all share the same sense. This paper describes an experiment which confirmed this hypothesis and found that the tendency to share sense in the same discourse is extremely strong (98%). This result can be used as an additional source of constraint for improving the performance of the word-sense disambiguation algorithm. In addition, it could also be used to help evaluate disambiguation algorithms that did not make use of the discourse constraint.