When I turn on the visual effects, the menu disappears border.

How to make when the effects enabled the menu have a border?

Interesting, my system has Desktop Effects enabled, yet shows the border as normal. Do you experience this behaviour under a new user?

Yes, I experience this behaviour under a new user.
First this happens in KDE 4.5. KDE 4.4 and earlier doesn't have this bug.

Not sure if the "oxygen-settings" application exists in KDE 4.5, but if it does you might find the option in there. It definitely exists in KDE 4.6.0, and upgrading to it is recommended.

I have KDE 4.6.2 and in "oxygen-settings" is settings for menu selections, but no settings for menu border.

Very unusual, do you experience this with KDE 4.6.3? Do you have Desktop Effects enabled, and if so does disabling them have any effect?

I see the same behavior in 4.6.2. There is still a white border, but it can't be seen in the screenshot for obvious reasons.

My guess is that the border should be replaced by a "real" shadow when composite is enabled. However, since I've disabled shadows, it shows no border at all on a white background.

I don't like shadows, but I want to use composite. How to make the normal borders in this case?

Unfortunately I have no idea, but I would guess that it's not configurable.

Can I fix it by editing source codes?

Yes, I'm pretty sure you can fix it in the source code. Not sure where, but I would start looking in the Oxygen style code.

Thanks, I'll wait.