A 5—CS rigid-body guidance linkage was proposed. A method to judge the defects of 5—CS linkage was proposed to solve the problems of defect judgment met in the process of rigid-body guidance design. Through calculating the Jacobian matrix’s determinant values of the given positions, it can be found out whether the signs of determinant values were changed at the given positions. If the signs were changed, the linkage had defects. If not, a curve tracking technique which based on Newton method was used to get the forward position solutions and then calculate the Jacobian matrix’s determinant values of the positions between the given positions. Based on the calculations, we can know whether there were positions which determinant values are zeros between the given positions. When the Jacobian matrix’s determinant value was zero, the linkage’s singular configuration occurred. According to the trajectory, we can clearly know whether the linkage has circuits or order defects. For solving the branch defect, the method of drives combinations was proposed. When the parameters of the linkage at a position were given, different Jacobian matrix’s determinant values can be got by selecting different drivers. So the branch defects can be avoided by changing the drive before the singular positions. Finally, a synthesis example was provided to illustrate the defect judgment process of 5—CS linkage.