This paper proposes a novel one-degree-of-freedom (1-DOF) deployable unit consisting of four parallelogram linkages. The unit is constructed by combining two 2Pa-3R (Pa: parallelogram linkage, R: revolute joint) deployable mechanisms and removing their 3R linkages. The kinematic properties of the resulting unit mechanism in the initially assembled configuration are analyzed in a global coordinate frame. It is shown that the angles between the normal vectors of the four shared nodes between parallelogram linkages remain constant, which implies that each node possesses a radial reciprocating motion capability. Furthermore, the mobility of the mechanism is investigated to examine the global preservation of kinematic properties. The analysis demonstrates that the proposed deployable unit is a single-DOF mechanism. This mobility characteristic does not violate the initial assembly conditions, so several desirable properties are maintained throughout the motion: the four shared nodes perform reciprocating motions with respect to a fixed point in space, and each pair of opposite shared nodes exhibits only 1-DOF relative translation along their connecting line. These important properties provide a solid basis for applying the proposed unit in a wider range of deployable structures and functional modules.