We report on an observation of transitions of the fourfold degenerate state of a magnetic vortex in soft magnetic nanodots by micromagnetic numerical calculations. The quaternary vortex states in patterned magnetic dots were found to be controllable by changing the density of out-of-plane dc or pulse currents applied to the dots. Each vortex state can be switched to any of the other states by applying different sequence combinations of individual single-step pulse currents. Each step pulse has a characteristic threshold current density and direction. This work offers a promising way for manipulating both the polarization and chirality of magnetic vortices.