Existence of normal bimagic squares

In this paper we provide a construction of normal bimagic squares by means of a magic pair of orthogonal general bimagic squares. It is shown that a normal bimagic square of order m n exists for all positive integers m , n such that m , n ∉ { 2 , 3 , 6 } and m ≡ n ( mod 2 ) , and a normal bimagic square of order 4 m exists if and only if m ≥ 2 .