Fall Detection (FD) has drawn the attention of the research community for several years. A possible solution relies on on-wrist wearable devices including tri-axial accelerometers performing FD autonomously. This type of approaches makes use of an event detection stage followed by some pre-processing and a final classification stage. The event detection stage is basically performed using thresholds or a combination of thresholds and finite state machines. In this research, a novel event detection is proposed avoiding the use of user predefined thresholds; this fact represents the main contribution of this study. It is worth noticing that avoiding the use of thresholds make solutions more general and easy to deploy. Moreover, a new set of features are extracted from a time window whenever a peak is detected, classifying it with a Neural Network. The proposal is evaluated using the UMA Fall, one of the publicly available simulated fall detection data sets. Results show the improvements in the event detection using the new proposal, outperforming the base line method; however, the classification stage still needs improvement. Future work includes introducing a finite state machine in the event detection method, adding extra features and a pre-classification of the post-peak interval and a better training configuration of the Neural Networks.