Objective. We propose a novel automated method called the S-Transform Gaussian Mixture detection algorithm (SGM) to detect high-frequency oscillations (HFO) combining the strengths of different families of previously published detectors. Approach. This algorithm does not depend on parameter tuning on a subject (or database) basis, uses time-frequency characteristics, and relies on non-supervised classification to determine if the events standing out from the baseline activity are HFO or not. SGM consists of three steps: the first stage computes the signal baseline using the entropy of the autocorrelation; the second uses the S-Transform to obtain several time-frequency features (area, entropy, and time and frequency widths); and in the third stage Gaussian mixture models cluster time-frequency features to decide if events correspond to HFO-like activity. To validate the SGM algorithm we tested its performance in simulated and real environments. Main results. We assessed the algorithm on a publicly available simulated stereoelectroencephalographic (SEEG) database with varying signal-to-noise ratios (SNR), obtaining very good results for medium and high SNR signals. We further tested the SGM algorithm on real signals from patients with focal epilepsy, in which HFO detection was performed visually by experts, yielding a high agreement between experts and SGM. Significance. The SGM algorithm displayed proper performance in simulated and real environments and therefore can be used for non-supervised detection of HFO. This non-supervised algorithm does not require previous labelling by experts or parameter adjustment depending on the subject or database considered. SGM is not a computationally intensive algorithm, making it suitable to detect and characterize HFO in long-term SEEG recordings.