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A holy alliance is wholly embarrassing.

The Illinois Supreme Court has a new chief justice, an appointment that under ordinary circumstances wouldn’t mean a whole lot.

That’s because the high court’s seven justices take turns handling the chief’s administrative duties. Every three years, a new chief replaces the old chief.

The outgoing chief is Lloyd Karmeier, a downstate Republican. The new one is Anne Burke, a Chicago Democrat.

If that name sounds familiar, perhaps linked to familial power politics, it’s because it should.

Anne Burke is married to indicted Chicago Alderman Ed Burke, one of that corrupt city’s leading politicos and the shady character at the center of a broad and ongoing federal corruption investigation.

Ed Burke faces charges of using his powerful office as a means of extorting legal business from a company seeking a city permit to renovate a restaurant in his district.

He also was the target of a wiretap that recorded thousands of his phone calls with various associates, some of which appear to be incriminating.

So while Ed Burke awaits his fate in the unfolding drama that court watchers predict will rock the city, Anne Burke will fulfill her role as one of the state’s leading jurists.

In any other state, the irony would be striking. But this is Illinois, a state where corruption and government walk hand in hand, although not always as clearly as the Burkes are demonstrating.