Co-clustering is a specific type of clustering that addresses the problem of finding groups of objects without necessarily considering all attributes. This technique has shown to have more consistent results in high-dimensional sparse data than traditional clustering. In trajectory co-clustering, the methods found in the literature have two main limitations: first, the space and time dimensions have to be constrained by user-defined thresholds; second, elements (trajectory points) are clustered ignoring the trajectory sequence, assuming that the points are independent among them. To address the limitations above, we propose a new trajectory co-clustering method for mining semantic trajectory co-clusters. It simultaneously clusters the trajectories and their elements taking into account the order in which they appear. This new method uses the element frequency to identify candidate co-clusters. Besides, it uses an objective cost function that automatically drives the co-clustering process, avoiding the need for constraining dimensions. We evaluate the proposed approach using real-world a publicly available dataset. The experimental results show that our proposal finds frequent and meaningful contiguous sequences revealing mobility patterns, thereby the most relevant elements.