We investigate the inherent timing properties of the timed token medium access control (MAC) protocol that are necessary for guaranteeing synchronous message deadlines in a timed token ring network such as the Fibre Distributed Data Interface (FDDI) network. As a result, the best-so-far result of the upper bound on the time possibly elapsed between any number of successive token arrivals at a particular node was derived. This result, which is particularly important for studies on real-time communications in any timed token ring network, has recently published in [see below] with no proof given due to space limitation. In this paper, we complement our early work by presenting a concise formal proof of this upper bound. The paper cited in "Abstract": S.Zhang and A.Burns, "An optimal synchronous bandwidth allocation scheme for guaranteeing synchronous message deadlines with the timed-token MAC protocol", IEEE/ACM Transactions on Networking, Vol.3, No.6, pp 729-741, December, 1995.