Dc-SQUID with Josephson junctions characterized by nonsinusoidal current-phase relation is being considered as a basis for phase qubit. It has been shown that the second and third harmonic components each in the current-phase relation are able to provide double-well potential and the energy level splitting. Threshold condition for the double-well form origin has been determined taking into account the impact of both harmonics. The splitting gap of the ground energy level has been calculated as a function of the harmonic amplitudes for different ratio s of characteristic Josephson energy E-C to the Coulomb energy E-Q0. It has been shown that the gap value comes to about 7E(Q0) with increase of the ratio s. No external field needed, no bias current required and no circular currents are major advantages of such a qubit. (c) 2006 Elsevier B.V. All rights reserved.