A novel systolic array for the nonsquare-root LDL^T method of Cholesky decomposition is presented. The systolic array is an alternative to that proposed by Brent and Luk; displaying an improvement in efficiency and a lower hardware cost, arising from a reduction in the number of multipliers required. An application for the array is in real-time digital signal processing hardware such as the modified covariance spectral estimator; which when used in conjunction with pulsed ultrasonic Doppler blood flow detectors, offers potentially improved sensitivity in the detection of atherosclerotic disease.