A new angles-only initial relative orbit determination (IROD) algorithm is derived using three line-of-sight observations. This algorithm accomplishes this by taking a Singular Value Decomposition of a 6x6 matrix to arrive at an approximate initial relative orbit determination solution. This involves the approximate solution of 6 polynomial equations in 6 unknowns. An iterative improvement algorithm is also derived that provides the exact solution, to numerical precision, of the 6 polynomial equations in 6 unknowns. The initial relative orbit algorithm is also expanded for more than three line-of-sight observations with an iterative improvement algorithm for more than three line-of-sight observations. The algorithm is tested for a range of relative motion cases in low earth orbit and geosynchronous orbit, with and without the inclusion of J2 perturbations and with camera measurement errors. The performance of the IROD algorithm is evaluated for these cases and show that the tool is most accurate at low inclinations and eccentricities. Results are also presented that show the importance of including J2 perturbations when modelling the relative orbital motion for accurate IROD estimates. This research was funded in part by the Air Force Research Lab, Albuquerque, NM.