Spacecraft formation flying has attracted an increasing amount attention over the past several decades including a growing interest in relative motion at the collinear lib ration points. This current work builds on previous efforts by further developing and characterizing a two-level targeting (TLT) algorithm used to determine relative motion at lib ration points by performing a convergence study. A parametric study was conducted to identify the sensitivity of the algorithm to a variety of inputs and constraints. The parametric study revealed that the two-level targeting algorithm convergence properties significantly improve when using a higher order initialization estimate. The size of the relative formation was also varied, and the algorithm was able to converge for formations ranging from 0.01 kilometers to 100 kilometers. The results also suggest that the patch point selection scheme and spacing contribute significantly to successful convergence. This study shows that the TLT approach has potential as a relative trajectory design tool for determining relative formations at lib ration points.