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It is shown that $\\Phi$ is strong skew commutativity preserving (that is, satisfies $\\Phi(A)\\Phi(B)-\\Phi(B)\\Phi(A)^*=AB-BA^*$ for all $A,B\\in{\\mathcal M}$) if and only if there exists some self-adjoint element $Z$ in the center of ${\\mathcal M}$ with $Z^2=I$ such that $\\Phi(A)=ZA$ for all $A\\in{\\mathcal M}$. 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