An accelerated procedure for the design of equiripple nonrecursive digital filters is described. The new procedure entails two techniques. The first technique is a selective search for the maxima of the error function, and it replaces the exhaustive search proposed by Rabiner, McClellan and Parks. It leads to a large saving in the number of function evaluations. The second technique is a more effective approach for the rejection of superfluous maxima of the error function. It can lead to a significant reduction in the number of iterations. The two techniques together lead to an overall saving in the amount of computation in the range 55 to 83%, depending on the filter specifications.