Yes

In "General" settings, under the signature text box, check the check-box that says

Insert this signature before quoted text in replies and remove the "--" line that precedes it.

Apparently this problem is known to Google:

The known issues page lists this:

Switching signatures doesn't work in plain text

Reported 29, October

It's possible to have unique signatures in Gmail for each sending address associated with your account. Currently, switching signatures when you change the "from" address of a message only works properly in rich text mode. Click Rich formatting at the top of the compose field to change modes.

Based on this, saving the signatures as rich text should help, but I don't have this button. So I have to wait, until Google fixes this.

Update: Google fixed it!

For me, it works again. It seems, that Google has fixed the problem.