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In a general decay chain $A\to B_1B_2\to C_1C_2\ldots$, we prove that theangular correlation function $I(\theta_1,\theta_2,\phi_+)$ in the decay of$B_{1,2}$ is irrelevant to the polarization of the mother particle $A$ atproduction. This guarantees that we can use these angular distributions todetermine the spin-parity nature of $A$ without knowing its production details.As an example, we investigate the decay of a potential doubly-charged boson$H^{\pm\pm}$ going to same-sign $\tau$ lepton pair.

A theorem about two-body decay and its application for a doubly-charged boson $H^{\pm\pm}$ going to $\tau^{\pm}\tau^{\pm}$