In this paper, a 2-D binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In ID, there is no 2-point LT with the symmetric basis vectors. Hence, in 2D, there is no 2 x 2-point separable ASLT. By taking non-separable BV basis images, this paper shows that a 2 x 2-point ASLT can be obtained. For its similarity to the Hadamard transform (HT), this paper refer to it as the lapped Hadamard transform (LHT). The efficient implementation is also given.