Abstract: Based on the coordinates of crystal axis，a reciprocal vector b*j ( j = 1，2，3 ) of a vector ai i = 1，2，3 ( ) is presented. By introducing the relatioanship bj = 2π b*j ，it is proved that bj is the basic vector of the reciprocal lattice，which is related to the direct lattice with basic vector ai . The matrix relationship of the basic vectors between the direct and the reciprocal lattices is equivalent to that definedin the textbook. This result indicates that the reciprocity of the basic vectors bj and ai embody in the duality property between the direct and the reciprocal lattices.

Key words: basic vector, reciprocal vector, matrix form, lattice