In this paper we study a possible symmetry in Sakata's model for the strongly interacting particles. In the limiting case in which the basic particles, proton, p, neutron, n and Λ-particle, Λ, have an equal mass, our theory holds the invariance under the exchange of p and Λ or n and Λ in addition to the usual charge independence and the conservation of electrical and hyperonic charge. From our theory the following are obtained: (a) iso-singlet π0′-meson state, which is a pseudo-scalar, exists, (b) the spin of Ξ-particle may be (3/2)+ and (c) several resonating states in K- and π-nucleon scattering are anticipated to exist.