Heart diseases are rapidly increasing worldwide and in our country. This increase causes difficulties in the diagnosis processes of heart diseases. Considering these problems, the studies of engineering applications related to medical science give effective results in terms of solutions. By means of engineering devices and algorithms, positive contributions are made to medical applications. These contributions assist physicians especially in the diagnosis stages and speed up these processes. In this study, a new algorithm is developped so that Atrial Fibrillation (AF), which is the most common type of arrhythmia encountered, can be automatically detected at a high success rate. Electrocardiogram (ECG) data used in this study were obtained from physiobank ATM database. 31 samples of Atrial Fibrillation Rhythm (AFR) and 31 samples of Normal Sinus Rhythm (NSR) were obtained from this database. RR Interval (RRI) sequences being 12 hours long are used in the study. The change of the RRI sequences is an important parameter for AF. The RRI sequences are re-sampled using signal pre-processing techniques. The Discrete Wavelet Transform (DWT) was then applied to the resampled signals. In this way, feature extraction process is performed and the wavelet energies of these signals are visually examined with boxplot. The wavelet energies of the RRI sequences are classified by the Support Vector Machine (SVM). Finally, AFR and NSR are successfully separated as 99.60% achievement.