We developed a simple method to eliminate electrocardiogram(ECG) artifacts from electroencephalogram(EEG) records by using simultaneously recorded ECG data. The raw EEG data, the real EEG data and the ECG data were regarded as multi-dimensional vectors Ea, Er and C, respectively. Also, the ECG data, with reduced amplitude whose coefficient was denoted as 'k', were assumed to be overlapped on the real EEG. These assumptions introduced the equations [Ea＝Er＋k･C], [Er･C＝0] and finally [k＝Ea･C/C･C]. This calculation method was implemented by a Macintosh computer using data exported from digital EEG recordings(sampled at 200Hz with 16-bit resolution). In several subjects, sampling intervals of 5 or 10 seconds for calculation succeeded in eliminating ECG artifacts. However, regardless of the sampling interval, this elimination condition was not always efficient in several other subjects, including a brain-dead patient. It was suggested that the ECG data used were insufficient for the calculation, because only one hand-to-hand reference was used for simultaneous recording, as usual. This one ECG reference was able to express only one ECG projection. Then two other hand-to-foot references of ECG were added to the recordings, and the elimination procedure was performed using all of the simultaneously recorded ECG data at the three references. Consequently, elimination was much improved in most subjects, includ-ing the brain-dead patient. Our method may be useful for eliminating ECG artifacts without changing reference electrodes.