The EDD connection admission control scheme has been proposed for supporting real-time communication in packet-switched networks. In the scheme, when a connection establishment request occurs, the worst-case link delay in each link along the connection is calculated to determine whether the request can be accepted or not. In order to calculate the worst-case link delay, we must perform a check called the point schedulability check for each of some discrete time instants (checkpoints). Therefore when there are many checkpoints, the worst-case link delay calculation is time-consuming. We have proposed a high-speed calculation method. The method finds some checkpoints for which the point schedulability check need not be performed and removes such unnecessary checkpoints in advance before a connection establishment request occurs, and the check is performed for each of the remaining checkpoints after the request occurs. However, the method is not so effective under the situation that the maximum packet length in networks is large, because the method can find few unnecessary checkpoints under the situation. This paper proposes a new high-speed calculation method. We relax the condition which determines whether or not the point schedulability check need not be performed for each checkpoint in our previous method and derive a new condition for finding unnecessary checkpoints. Using the proposed method based on the new condition, we can increase the number of unnecessary checkpoints compared to our previous method. Numerical examples which are obtained by extensive simulation show that the proposed method can attain as much as about 50 times speedup.