1. College of Mathematics and Information Sciences, Henan University2. The Fifth Middle School of Guangzhou

Abstract: In these two papers (I) and (II), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (I), we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.

Key words: Yang-Baxter equation, quantum Yang-Baxter function equation