Electrocardiograms (ECG) provide invaluable insight into the conditions of the heart and are widely used for diagnosing cardiac diseases. Recent advances in miniature sensors and low-power wireless transmitters make body area sensor networks (BASN) a compelling platform for mobile ECG monitoring. However, energy efficiency is still one of the major issues in BASN, which are typically battery-powered. In this paper, we present an innovative and energy-efficient Pre-Diagnosing ECG Transmission Technique for BASN. In our technique, we explore the differences of ECG data in terms of its importance for medical diagnosis. A self-learning ECG classification algorithm is designed to classify the sensed ECG data into the three classes of abnormal heart beats, unknown heart beats and normal heart beats. Subsequently, the communication resources are allocated differently on these heart beat classes so that communication energy can be saved without affecting the cardiac disease monitoring and diagnosis. According to our test results, about 80% to 100% classification accuracy can be achieved, with 0% misses in abnormal heart beats, while saving about 76% of energy compared with non-classifying transmission techniques in transmitting normal heart beats.