The coterie join operation proposed by Neilsen and Mizuno produces, from a k-coterie and a coterie, a new k-coterie. For the coterie join operation, this paper first shows 1) a necessary and sufficient condition to produce a nondominated k-coterie (more accurately, a nondominated k-semicoterie satisfying Nonintersection Property) and 2) a sufficient condition to produce a k-conterie with higher availability. By recursively applying the coterie join operation in such a way that the above conditions hold, we define nondominated k-coteries, called tree structured k-coteries, the availabilities of which are thus expected to be very high. This paper then proposes a new k-mutual exclusion algorithm that effectively uses a tree structured k-coterie, by extending Agrawal and El Abbadi's tree algoriyhm. The number of messages necessary for k processes obeying the algorithm to simultaneously enter the critical section is approximately bounded by k log (n / k) in the best case, where n is the number of processes in the system.