In this paper, we consider the (N, K, L) multi-access caching network where K users and K caches are connected to a server with N files, each of size F bits, through a shared error-free broadcast channel. Each user has access to L nearby caches, each of size M F bits, in a cyclic wrap-around manner. Even after several previous attempts, the exact characterization of the optimal rate memory tradeoff is still an open problem except in the case where L = K-1 and L = 1 with large cache M ∈ [ N/L.(K-1)/K, N/L ]. This paper determines the optimal rate memory tradeoff for the cache network with L = K-2 and M ∈ [ N/(K-2). (K-1)/ K , N/(K-2) ]. This is done by proposing a new caching scheme that operates at the memory rate pair (N /(K-2). (K-1)/ K , 1/K) and deriving a set of lower bounds to demonstrate the optimality of the scheme.