Mobile communication has grown quickly in the last two decades. Connections can be wirelessly established from almost any habitable place in the earth, leading to a plethora of connection-based tracking mechanisms, such as GPS, GSM, RFID, etc. Trajectories representing the movement of people are consequently being gathered and analysed in a daily basis. However, a trajectory may contain sensitive and private information, which raises the problem of whether spatio-temporal data can be published in a private manner.In this article, we introduce a novel distance measure for trajectories that captures both aspect of the microaggregation process, namely clustering and obfuscation. Based on this distance measure we propose a trajectory anonymisation heuristic method ensuring that each trajectory is indistinguishable from $$k-1$$ other trajectories. The proposed distance measure is loosely based on the Fréchet distance, yet it can be computed efficiently in quadratic time complexity. Empirical studies on synthetic trajectories show that our anonymisation approach improves previous work in terms of utility without sacrificing privacy.