We show that for an arbitrary unimodular lattice Λ of dimension n and an arbitrary point C =(c1, c2...cn) ɛ Rn a point Y = (y1, y2,..., yn) e Λ can be found and also a number h, satisfying the condition 1 ⩽h ⩽ 2−n/2 θ−1 + 1 (0 < θ ⩽ 2−n/2), such that the inequality $$\prod\nolimits_{i = 1}^n {\left| {Y_i + hc_i } \right|}< \theta $$ will be satisfied.