In this paper, analytic singularity analysis of a 4-DOF parallel robot H4 is addressed. Since a parallel manipulator consisting of several serial chains has complex singularities in the workspace, the determination of singular configurations is very important in design, trajectory planning, and control. The classical method to determine singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general and thus it is not easy to find the determinant of the Jacobian matrix. Therefore, we focus on the analytic singularity analysis of a 4-DOF parallel robot H4 using Jacobian deficiencies. A subset of the whole singularities and the intuitively predictable ones are only derived using Jacobian matrix deficiency. Three type singularities, i.eo, overmobility, undermobility and combined singularities, have been presented.