An e-mail relay apparatus notifies a user of which e-mail could not be transmitted if a transmission error has occurred, without consuming a memory capacity. When an e-mail transmission instruction is received and after header information of the received e-mail is stored, a digital signature is added to the e-mail, and the e-mail text is encrypted. Then, after the digital signature is added, the encrypted e-mail is stored, and after the original e-mail is deleted, the transmission of the e-mail is started. If an error has occurred during the e-mail transmission and the transmission has failed, an error-notifying mail addressed to a transmission source is generated. After a header file of the e-mail is attached to the error-notifying mail, the error-notifying mail to which the header file is attached is stored in a mail box for the user of the transmission source.