Abstract: In [1, 1.7], Shi defined an equivalent relation on the set of all simple root systems of a finite complex reflection group G. Shi also gave all non-equivalent simple root systems of G with G ∈{G₁₂, G₂₄}. In this paper, we found all the non-equivalent simple root systems of G with G ∈{G₁₃,G₂₂,G₂₇,G₂₉,G₃₁,G₃₃}.

Key words: simple root system, equivalent simple root systems, complex reflection group, root system, simple root system, equivalent simple root systems, complex reflection group