Topological charge (TC) of an optical vortex (OV) is a crucial parameter. We propose two factors, namely, the phase jump factor and the phase gradient factor, to replace the parameter of TC through unwrapping the TC definition integral. Based on these two factors, we report on a novel OV, referred to as the remainder-phase optical vortex (ROV). The properties of the ROV are studied in depth by adjusting these two factors. Results show that the phase gradient factor determines the total orbital angular momentum (OAM), whereas the phase jump factor decides the number of split unit vortices and reshapes the structure of the OAM distribution. This work provides a novel OV with controllable OAM distribution, which will open up new applications such as particle manipulation, beam shaping, and micro-fabrication. (C) 2019 Optical Society of America