This paper proposes a ternary subset difference method (SD method) that is resistant to coalition attacks. In order to realize a secure ternary SD method, we design a new cover-finding algorithm, label assignment algorithm, and encryption algorithm. These algorithms are required to revoke one or two subtrees simultaneously while maintaining resistance against coalition attacks. We realize this two-way revocation mechanism by creatively using labels and hashed labels. Then, we evaluate the efficiency and security of the ternary SD method. We show that the upper bound of the average message length in the ternary SD method is smaller by about 12.2 percent than that of the conventional SD method, and the number of labels on each client device can be reduced by about 20.4 percent. On the other hand, the computational cost imposed on a client device stays within O(logn). Finally, we prove that the ternary SD method is secure against coalition attacks.