Detection of QRS complex in electrocardiogram (ECG) signals is of immense importance in cardiac health prognosis. In this paper a new symmetric wavelet for detection of R-peak is presented, which has been designed based on spectral characteristics and morphology of QRS complex. The detection of R-peak was carried out using this designed wavelet, and with existing symmetric wavelets such as db3, db6, haar and bior2.2. The detection accuracy with this wavelet is 99.99%, which is higher than those with existing symmetric wavelets. The algorithm has been tested on standard databases such as Fantasia database of normal and healthy subjects, MIT/BIH (Massachusetts Institute of Technology/Beth Israel Hospital) arrhythmia database, and on self-recorded electrocardiograms of normal subjects and patients under diseased stress. The study of heart rate variability (HRV) through computation of RR-tachogram using the new wavelet has proved to be effective in reliably evaluating HRV parameters.