The major problem in an ultrasonic flaw detection system is the presence of microstructure noise (clutter) resulting from scattering at grain boundaries. Ultrasonic grain echoes are random in amplitude and arrival time and often interfere and mask the flaw echo. Grain echoes are stationary and correlated from scan to scan in the same propagation path. An effective method of decorrelating grain echoes can be achieved by changing the frequency from scan to scan, a method known as frequency diversity. In practice frequency diverse grain echoes can be obtained by transmitting a broadband echo through the materials and bandpass filtering the received echoes over many bands of frequencies. At any given time the outputs of bandpass filters are the features representing information related to flaw or grain echoes. Although these outputs are random, the statistics of flaws and grains echoes are different. This situation permits application of statistical pattern recognition using a Bayes classifier. Experimental data and computer simulation have confirmed that flaw and clutter echoes over different frequency bands have a Gaussian distribution with different covariance matrices. For this situation the Bayes classifier is quadratic and provides optimal flaw detection performance. Presented here is the design of an optimal classifier with experimental and simulated results.