The analysis of robot dextrous workspace is a problem of robot kinematics which is not solved today.Because the operations of robot are not limited by its mechanism in dextrous workspace, the size of robot dextrous workspace seems very important in developing its operating properties. This paper deals with the calculation problem of the boundary of manipulator dextrous workspace. First, it analyses the nature of the boundary of dextrous workspace. Secondly, it determines the boundary of dextrous workspace in proj-ect plane with a new method. Lastly, it presents a method of computation of the end boundary of dextrous workspace.