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Let $\varphi$ and $\psi$ be holomorphic self-maps of the unit disk, and denote by $C_{\varphi }$, $C_{\psi }$ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators $C_{\varphi }-C_{\psi }$ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.