Several algorithms have been proposed in the last years for discovering stops in trajectories of moving objects. Some methods consider as stops the subtrajectories that i) have speed lower than the average trajectory speed, ii) present significant direction changes, iii) have gaps, or iv) intersect a given spatial region. In these approaches a time constraint should be met for the subtrajectory to be considered as a stop, and this constraint is absolute (it is met or not). Indeed, these approaches consider stops as a continuous subtrajectory. In this paper, we show that for several application domains the stops do not need to be continuous, and the time constraint should be relaxed. In summary, we present the definitions of non-continuous stops and present an algorithm to discover a new kind of stops. We evaluate the proposed algorithm with a running example and real trajectory data, comparing it to the most similar approach in the literature, the SMoT algorithm.