The non-compression brace has been investigated and developed as a new earthquake-resistant structural member by the authors. The Z-type brace shows one-side seismic responses of the structure controlled by the function of the wedge-device. In this paper, an anti-symmetric Z-type braced frame subjected to seismic loadings shows torsional vibration. The braced frame in one-directional ground motions can absorb the plastic energy by twisting deformation.