system
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There is an easy way, though it will cause the “Avast, Virus Database Has Been Updated” announcements to be eliminated as well (which I find acceptable).
Open the Avast UI by clicking the ball in the System Tray, then choose Settings, then Update. In the Details section, UNcheck the [ ] Show notification box after automatic update setting, then OK out.
You may want to check to see that the setting has “stuck” after you changed it. I had a case where it didn’t, and had to completely uninstall and reinstall Avast before the setting would stick.
-Noel