Accelerometer signals generated through gait present a new frontier of human interface with mobile devices. Gait cycle detection based on these signals has applications in various areas, including authentication, health monitoring, and activity detection. Template-based studies focus on how the entire gait cycle represents walking patterns, but these are compute-intensive. Aggregate feature-based studies extract features in the time domain and frequency domain from the entire gait cycle to reduce the number of features. However, these methods may miss critical structural information needed to appropriately represent the intricacies of walking patterns. To the best of our knowledge, no study has formally proposed a structure to capture variations within gait cycles or phases from accelerometer readings. We propose a new structure named the PQRST Complex, which corresponds to the swing phase in a gait cycle and matches the foot movements during this phase, thus capturing the changes in foot position. In our experiments, based on the nine features derived from this structure, the accelerometer-based gait authentication system outperforms many state-of-the-art gait cycle-based authentication systems. Our work opens up a new paradigm of capturing the structure of gait and opens multiple areas of research and practice using gait analogous to the "QRS complex" structure of ECG signals related to the heart.