This paper discusses how to further refine the minimalist theory of Chomsky (1995). First of all, it is claimed that the minimalist theory should be refined in terms of non-determinism rather than in terms of determinism though Chomsky(1995. 2008) claims that the determinism should be maintained for the minimalist theory. For example, in this paper it is argued that the deterministic notion of edge feature posited in Chomsky (2008) should be eliminated in order to maintain the non-determinism, which even leads to derivational null hypothesis. And it is further argued that global non-determinism may lead to cover the notion of PF-only interpretive effects as well as the notion of LF-only interpretive effects. In fact, some variability of interpretive effects may never be strictly covered by any simple theory of determinism. For example, some phenomena of non-determinism lead to postulation of the so-called syntactic parallel movements. Furthermore, there are cases of non-determinism which entail the postulation of null hypothesis for the minimalist theory.
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