A method for a geographical hot redundancy between a first safety computer and a second safety computer, the first and second safety computers being remote from each other to avoid failure common modes, the first and second safety computers being connected to each other by a generic communication network without a synchronisation link allowing a strict synchronisation between the first and the second safety computers, the first safety computer cyclically executing a first replica of an application and the second safety computer, providing a redundancy for the first safety computer, cyclically executing a second replica of said application, the method being characterized by the steps consisting in, in normal operation, while the first safety computer operates as a master computer and the second safety computer operates as a slave computer,: - a) a transmission by the first safety computer to the second safety computer of a message (M N) comprising first input data items for an n th cycle and all or part of a first execution context of the application for the n th cycle; - b) an execution, during the n th cycle, of the first replica of the application on the first safety computer and updating of the first execution context of the application at the end of the n th cycle; - c) a transmission by the first safety computer to the second safety computer of a first output quantity (S N) corresponding to all or part of the first execution context at the end of the n th cycle; - d) a reception by the second safety computer of the message (M N) and a recovery of the first input data items for the n th cycle and of all or part of the first execution context for the n th cycle contained in the message as second input data items and a second execution context for the n th cycle on the second safety computer; - e) an execution, during the n th cycle, of the second replica of the application on the second safety computer in the second execution context for the n th cycle, on the second input data items of the n th cycle, and an update of the second execution context at the end of the n th cycle; - f) a check and verification, preferably by the second safety computer, of the consistency between the first and second safety computers by comparing a second output quantity (S' N) corresponding to all or part of the second execution context at the end of the n th cycle on the second safety computer with a first output quantity (S N) at the end of the n th cycle received from the first safety computer. - a) a transmission by the first safety computer to the second safety computer of a message (M N) comprising first input data items for an n th cycle and all or part of a first execution context of the application for the n th cycle; - b) an execution, during the n th cycle, of the first replica of the application on the first safety computer and updating of the first execution context of the application at the end of the n th cycle; - c) a transmission by the first safety computer to the second safety computer of a first output quantity (S N) corresponding to all or part of the first execution context at the end of the n th cycle; - d) a reception by the second safety computer of the message (M N) and a recovery of the first input data items for the n th cycle and of all or part of the first execution context for the n th cycle contained in the message as second input data items and a second execution context for the n th cycle on the second safety computer; - e) an execution, during the n th cycle, of the second replica of the application on the second safety computer in the second execution context for the n th cycle, on the second input data items of the n th cycle, and an update of the second execution context at the end of the n th cycle; - f) a check and verification, preferably by the second safety computer, of the consistency between the first and second safety computers by comparing a second output quantity (S' N) corresponding to all or part of the second execution context at the end of the n th cycle on the second safety computer with a first output quantity (S N) at the end of the n th cycle received from the first safety computer.