Abstract Maneuvering a relativistic starship is not as easy as it appears. The closer is its velocity to the speed of light the less maneuverable it appears to be relative to the rest frame. The relativistic kinematic equations are derived and the examples of starship trajectories are calculated on the condition of a constant proper acceleration and taking into account the required protection from hard radiation caused by the oncoming relativistic flow of interstellar gas. Possible navigation methods are also outlined shortly.