In a method and arrangement for the secure transmission of at least one electronic message from a first terminal of a first user to at least one second terminal of a second user, the electronic message is generated by the first terminal. The electronic message is received by the second terminal. The electronic message is transmitted by an infrastructure for legally binding transmission of electronic messages from the first terminal to the second terminal. A first security module connected to the first terminal encrypts and/or signs the electronic message before the electronic message is transmitted by the infrastructure from the first terminal to the second terminal. A second security module, connected to the second terminal, decrypts the transmitted electronic message and/or verifies the signed electronic message.