A substitution box (s-box) is a nonlinear component function used in most block ciphers. It must fulfill several cryptographic properties such as high nonlinearity, low differential uniformity and complex algebraic expression to resist against linear, differential and interpolation attacks. In this paper, we extend and improve the s-box construction method proposed by Mamadolimov et al. [26, 27] which construct an s-box from power and binomial functions over the finite field F28. We study the cryptographic properties exhibited from our s-box and do a comparative analysis with several known 8×8 bijective s-boxes. Our analysis shows that our proposed s-box is ranked seventh compared to known 8×8 bijective s-boxes in terms of strong cryptographic properties. It even surpasses some known s-boxes used in popular block ciphers.