In this paper, a novel four-variable refined theory of plate, called RPT, has been proposed for free vibration of composite laminated plates, using a hyperbolic sine function, for calculating out-of-plane shear strains. It is one of the properties of this theory that the boundary condition of zero shear stress is satisfied over upper layer and under lower layer of plate, with no reference to Timoshenko shape factor. In contrast to other higher-order shear deformation theories, in RPT theory, equations of motion are coupled dynamically only in inertial terms, while elastic energy terms are not coupled for the variables used. From this viewpoint, RPT theory is similar to classical plate theory (CLPT). Some of the objectives of this paper are the investigation of effect of influential parameters on fundamental frequency, such as modulus ratio, angle of plies, and plate length-to-thickness ratio. The results of this proposed version of RPT are compared and validated with those of first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT), and the original version of RPT.