The method of determining the position of a radio-frequency signal receiver consists first of all in dividing the Earth's surface into N geographical regions as a function of the N channels available in the correlation stage of the receiver. At least one satellite in projection onto the Earth's surface has to be located in each of the N defined regions. The N channels of the correlation stage are each configured and switched on to search for a visible satellite in one of the N respective regions. Radio-frequency signal reception and shaping means pick up said radio-frequency signals and frequency convert them to provide intermediate signals to the correlation stage. Once one of the channels has detected a visible satellite in one of the N regions, the operation of all the other channels is interrupted by a stop block located in each of the other channels. Subsequently, certain other channels are configured and switched on for searching and tracking visible satellites in proximity to the first detected visible satellite. This allows precise position and time calculations to be made in the microprocessor means of the receiver. An approximate position is calculated as soon as at least four satellites are tracked by a direct method, before calculating the precise position of the receiver by a conventional iterative method.