In this study, a novel form of the Kerr solution is presented. The solution comprises a time coordinate which signifies the local appropriate time for the free-falling viewers on a set of the simple trajectories. Various physical events are chiefly clear when associated to this time coordinate. The selected coordinates also confirm that the solution is well performed at the horizon. The solution is well fit to the tetrad formalism and a suitable null tetrad is existing. Also given the Dirac Hamiltonian and, for one choice of the tetrad, it contains on a simple, Hermitian form.