From the Pelican Parts write up
http://www.pelicanparts.com/BMW/tech...de_Reading.htm . "When you are finished reading the codes, you can reset the computer and clear them all out. Make sure that the last code (1000) has occurred, and then press down on the gas pedal for more than 10 seconds. This should clear out the memory of the DME. Repeat the fault code reading process, and the computer should generate code 1444, which means that there are no faults stored."
Of course that supposes that the system gives you a last code instead of just continuing to blink.
There is a link off this page
http://www.pelicanparts.com/BMW/tech...nostics%20.htm that suggests there are differences between OBD I systems on different BMWs. Importantly since there are few 318ti owners with the OBD I systems, there is an email for the author inviting questions. Sounds like time to ask an expert