Robustly detecting steps with inertial sensors em- bedded in smartphones remains a challenging problem for pedestrian navigation, mainly due to the diversity of human gaits. In this paper, we propose a new step detection method for handheld devices, smartSTEP, that processes acceleration and gyroscope signals with machine learning techniques. The advantage of smartSTEP is that it does not rely on hand motion mode classifiers nor thresholds calibration. Trained on 9000 steps from 12 different participants and tested on approximately 2200 steps recorded on persons mostly not involved in the training, it achieved 99% recall and 98.9% precision in challenging scenarios such as asymmetrical walking, outdoor walking on different surfaces with different hand motion modes, and stairs climbing. A 0.097 seconds root mean square error is achieved on the predicted stride duration. This competes with the performances of present algorithms dedicated to calculating stride duration.