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We present a new method for analyzing eye diagrams that always provides a unique solution by making use of a robust, least-median-of-squares (LMS) location estimator. In contrast to commonly used histogram techniques, the LMS procedure is insensitive to outliers and data distributions. Our motivation for developing this algorithm is to create an independent, benchmark method that is both amenable to a thorough uncertainty analysis and can function as a comparison tool since no standardized industry algorithms currently exist. Utilizing this technique, we calculate the fundamental parameters of an eye diagram, namely the one and zero levels, and the time and amplitude crossings. With these parameters determined, we can derive various performance metrics, such as extinction ratio and root-mean-square jitter, and perform eye-mask alignment. In addition to describing our algorithm in detail, we compare results computed with this method to those of a commercial oscilloscope, and obtain excellent agreement. Finally, we suggest new definitions of eye height and eye width that are more robust than those that are commonly used.