In this paper, the problem of detecting narrow lines embedded in correlated noise is investigated. An approach based on the contrast theory is adapted to the four-way Graeco-Latin squares design. The analysis provides a theoretical basis for the comparison of a line detector to other detectors that ignore noise dependence. A new and compensated algorithm is developed for detecting lines oriented in any major direction in a two-dimensional image plane. The four-way design is also shown to remove any background obscuration, and the actual processor is robust, simple, efficient, and suitable for real-time applications. Extensive computer simulations demonstrate the performance of the proposed detector relative to some classical mask-based detectors.