The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.