Let T be an n-dimensional complex torus with an automophism g. Let A Є GL_n (C) be the complex representation of g and α_1,...,α_n be the eigenvalues of A. Then it is clear that α_i, i=1,..., n, are units of algebraic number fields of degree ≦ 2n. It seems to be interesting to study the structure of T in case α_i, i=1,..., n, have degree 2n. We have studied the structure in detail when n=2, [3], [4], so in this note we try to investigate the structure when n≧3.