Setting of this investigation is Bishop?s constructive mathematics. Notions of QA-mappings and Q-quasi-antiorders were introduced and studied by the author in a recent article. Yet another theorem on antiordered semigroups is given in this paper. Let Sand Tbe antiordered semigroups, dbe a Q-quasi-antiorder on Tand ?be a QA-homomorphism of Sonto T. Then if sis a Q-quasi-antiorder on Ssatisfying ?there exists a unique QA-homomorphism y of ?onto

constructive mathematics, semigroup with apartness, antiorder, quasi-antiorder, isotone and reverse isotone homomorphism.