A machine-learning classifier for radiation waveforms of negative return strokes (RSs) is built and tested based on the Random Forest classifier using a large dataset consisting of 14,898 negative RSs and 159,277 intracloud (IC) pulses with 3-D location information. Eleven simple parameters including three parameters related with pulse characteristics and eight parameters related with the relative strength of pulses are defined to build the classifier. Two parameters for the evaluation of the classifier performance are also defined, including the classification accuracy, which is the percentage of true RSs in all classified RSs, and the identification efficiency, which is the percentage of correctly classified RSs in all true RSs. The tradeoff between the accuracy and the efficiency is examined and simple methods to tune the tradeoff are developed. The classifier achieved the best overall performance with an accuracy of 98.84% and an efficiency of 98.81%. With the same technique, the classifier for positive RSs is also built and tested using a dataset consisting of 8,700 positive RSs. The classifier has an accuracy of 99.04% and an efficiency of 98.37%. We also demonstrate that our classifiers can be readily used in various lightning location systems. By examining misclassified waveforms, we show evidence that some RSs and IC discharges produce special radiation waveforms that are almost impossible to correctly classify without 3-D location information, resulting in a fundamental difficulty to achieve very high accuracy and efficiency in the classification of lightning radiation waveforms.