Let A be an n × n real matrix. We define orthogonal similarity-transversality property (OSTP) if the smooth manifold consisting of the real matrices orthogonally similar to A and the smooth manifold Q(sgn(A)) (consisting of all real matrices having the same sign pattern as A), both considered as embedded smooth submanifolds of R^{n × n}, intersect transversally at A. More specifically, with S = [s_ij ] being the n×n generic skew-symmetric matrix whose strictly lower (or upper) triangular entries are regarded as independent free variables, we say that A has the OSTP if the Jacobian matrix of the entries of AS − SA at the zero entry positions of A with respect to the strictly lower (or upper) triangular entries of S has full row rank. We also formulate several properties like OSTP2 and show that if a matrix A has the OSTP, then every superpattern of the sign pattern sgn(A) allows a matrix orthogonally similar to A, and every matrix sufficiently close to A also has the OSTP. This approach provides a theoretical foundation for constructing matrices orthogonally similar to a given matrix while the entries have certain desired signs or zero-nonzero restrictions. In particular, several important classes of zero-nonzero patterns and sign patterns that require or allow the OSTP are identified, and we gives several examples illustrating some applications.