Let \({\mathcal A}_ n(-1,1)\) be the set of all matrices of order n with elements from \(\{\)-1,1\(\}\). Let \(U_ n=\{\det A|\) \(A\in {\mathcal A}_ n(-1,1)\}\), which is a finite set of integers. Two questions are considered: (i) Which is the biggest (resp. the smallest) number from \(U_ n?\); (ii) If \(a_ n\) (resp. \(b_ n)\) is the biggest (resp. the smallest) element of \(U_ n\), which is the number of matrices \(A\in {\mathcal A}_ n(-1,1)\) such that det A\(=a_ n\) (resp. det A\(=b_ n)?\) In the first part of the paper by the first author and S. Dăncescu [Gaz. Mat. Bucur. 89, No.4-5, 130-134 (1984; reviewed above)], the answer to (i) and (ii) for \(n=3\) is given. The present paper answers to questions (i) and (ii) for \(n=4\) and only to question (i) for \(n=5\).