An automated method for detecting and eliminating electrocardiograph (ECG) artifacts from electroencephalography (EEG) without an additional synchronous ECG channel is proposed in this paper. Considering the properties of wavelet filters and the relationship between wavelet basis and characteristics of ECG artifacts, the concepts for selecting a suitable wavelet basis and scales used in the process are developed. The analysis via the selected basis is without suffering time shift for decomposition and detection/elimination procedures after wavelet transformation. The detection rates, above 97.5% for MIT/BIH and NTUH recordings, show a pretty good performance in ECG artifact detection and elimination.