In the method a graphical password is produced for an electronic system, such as a database, a computer program or Internet pages, the password being composed of various identifier images that are clearly distinguishable from each other. The system can be located in a terminal device used by the user, such as a mobile phone or an object separate from the terminal device, to which the user can be connected via the terminal device. For producing the password, the electronic system includes an image archive, in which various partial images representing certain subareas of a whole identifier image have been saved in electronic form. The partial images are divided into subgroups so that the partial images of the same subgroup always represent the same subarea of the identifier image. The identifier images belonging to the graphical password are composed by selecting partial images from different subgroups and by combining the selected partial images into one complete identifier image.