We present a new block adaptive algorithm as a variant of the Toeplitz-preconditioned optimum block adaptive (TOBA) algorithm. The proposed algorithm is formulated by combining the TOBA algorithm with a data-reusing scheme that is realized by processing blocks of data in an overlapping manner, as in the optimum block adaptive shifting (OBAS) algorithm, Simulation results show that the proposed algorithm is superior to the OBAS and TOBA algorithms in both convergence rate and tracking property of input signal conditioning.