Continuous sharing of users’ location information is vital for decision-making applications, such as smart health care, smart traffic analysis, etc. Since this data originates from users’ private information, protecting their privacy is crucial. Local Differential Privacy is a modified version of standard differential privacy that enables users to anony mize their location data before transmission to service providers or applications, thus safeguarding users’ privacy even in the presence of hostile service providers. However, The LDP approach offers strong privacy protection against threats or attacks by assuming that a user’s location data points are independent of one another. But in fact, the location data points of a user may be correlated, which increases privacy risks because traditional LDP does not provide enough privacy budget for these correlated data points in order to gain strict privacy. To address this challenge, our paper proposes a approach for distributing a adequate budget to correlated data points and proving that our approach achieves LDP across an infinite user location stream. Our proposed met hod comprises two phases: first, computing dissimilarity between current and previous published location information, and second, based on the dissimilarity computed in the first phase, the method makes a decision on whether to publish the current location data point or a null publication. Finally, we tested our method using real and simulated datasets, and the results show that it guarantees LDP privacy for users, regardless of whether their location data points are correlated. And also improves data utility as compared with existing methods.