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Detection of Electrocardiogram (ECG) characteristic points can provide critical diagnostic information about heart diseases. We propose a novel feature extraction and machine learning scheme for ECG delineation. A new feature, termed as randomly selected wavelet transform (RSWT), is proposed to effectively represent ECG morphology. With the RSWT feature pool, a regression tree is trained to estimate the probability distribution to the direction toward the target point, relative to the current position. The continual random walk through 1D space will eventually produce a reliable region from which the final position of the target point is derived. The evaluation results on QT database show better detection accuracy compared with other studies while providing real-time processing capability.