A method of monitoring movements of an individual or object provided with a direction indicator that is adapted to send to a monitoring center from a mechanical or electronic sensor a signal that discloses the direction of the direction indicator so as to enable, together with other signals sent to the monitoring center and disclosing the position of the individual object, which is shown on a display screen in the form of a correctly-turned three-dimensional animated picture. The direction indicator includes an indicating element which is adapted to take essentially the same position regardless of the orientation of the direction indicator. The direction indicator includes sensors for sensing the position of the indicating element and producing a signal that can be sent to a monitoring unit which shows the direction of the individual or object carrying the direction indicator.