When associationrules A → B and A → C cannot be discovered from the database, it does not mean that A → B ∨ C will not be an associationrule from the same database. In fact, when A, B or C is the newly marketed product, A → B ∨ C shall be a very useful rule in some cases. Since the consequent item of this kind of rule is formed by a disjunctive composite item, we call this type of rules as the disjunctiveconsequentassociationrules. Therefore, we propose a simple but efficient algorithm to discover this type of rules. Moreover, when we apply our algorithm to insurance policy for cross selling, the useful results have been proven by the insurance company.