Accurate frequency-domain system identification demands for reliable computational algorithms. The aim of this paper is to develop a new algorithm for parametric system identification with favorable convergence properties and optimal numerical conditioning. Recent results in frequency-domain instrumental variable identification are exploited, which lead to enhanced convergence properties compared to classical identification algorithms. In addition, bi-orthonormal polynomials with respect to a data-dependent bi-linear form are introduced for system identification. Hereby, optimal numerical conditioning of the relevant system of equations is achieved. This is shown to be particularly important for the class of instrumental variable algorithms, for which numerical conditioning is typically quadratic compared to alternative frequency-domain identification algorithms. Superiority of the proposed algorithm is demonstrated by means of both simulation and experimental results.