By introducing the biinfinite symbol vector space， the dynamical properties of elementary cellular automata rule 40 with minority memory are in depth studied from the symbolic dynamics perspective. Using computer programming， we get a subsystem with Bernoulli right shift. Then topological mixture and topological entropy on the subsystem are analyzed by the transition matrix， which is determined by the twoorder subshift of finite type. Furthermore， we indicate that it is chaotic in the sense of both LiYorke and Devaney on the subsystem. Finally， the method presented in this paper is also applicable to other cellular automata.