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It is proved by purely algebraic method that weakly conformal,conformal and A3z=0 are mutually equivalent if φ∶Ω→CPn is a non-isotropic harmonic map and the harmonic maps with isotropy order ≥3 are uniquely determined by a system of ordinary differential equations. A method is given, by which the isotropy orders of non-isotropic harmonic maps can be computed.