One way is to mute the volume on the phone. The other way is permanently delete the file at /system/media/audio/ui/camera_click.ogg.

The problem I have is the file is read only file and ASTRO File Manager could not delete it. I think the only way to delete it is to use Android Debug Bridge and sent these commands:

1) adb remount
2) adb shell rm /system/media/audio/ui/camera_click.ogg.

My problem now, I do not know how to use that ADB!