The increasing abundance of data about the trajectories of personal movement is opening up new opportunities for analyzing and mining human mobility, but new risks emerge since it opens new ways of intruding into personal privacy. Representing the personal movements as sequences of places visited by a person during her/his movements -semantic trajectory -poses even greater privacy threats w.r.t. raw geometric location data. In this paper we propose a privacy model defining the attack model of semantic trajectory linking, together with a privacy notion, called c-safety. This method provides an upper bound to the probability of inferring that a given person, observed in a sequence of nonsensitive places, has also stopped in any sensitive location. Coherently with the privacy model, we propose an algorithm for transforming any dataset of semantic trajectories into a c-safe one. We report a study on a real-life GPS trajectory dataset to show how our algorithm preserves interesting quality/utility measures of the original trajectories, such as sequential pattern mining results.