If the Federal Reserve screws up in exiting from its massive stimulus, the results could be very harmful for the global economy, warns OppenheimerFunds CEO Bill Glavin.

The Fed has trimmed its bond purchases to $45 billion a month from $85 billion last year and is expected to finish quantitative easing (QE) by October or December. Then the central bank is expected to raise interest rates, perhaps beginning in the second half of next year.

And the Fed now has a balance sheet of more than $4 trillion to unwind.

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"We're all counting on the Fed threading the needle. I mean, it's not just for bond investors, frankly. It's for the world economy," Glavin tells CNBC.

"If they're clumsy in their unwinding, that will spike rates and that will have very negative impacts on the global economy."

But Glavin said the Fed has handled things well so far, with its tapering of QE. "Generally I think they're on the right track, and I think we have a long way to go," he notes.

Meanwhile, Alan Blinder, former vice chairman of the Fed, says we should expect internal conflict at the central bank as it proceeds in reversing its easing.

When QE nears an end, "financial markets will fixate completely on the Fed's eventual exit from its current extraordinarily easy monetary policy," he writes in The Wall Street Journal.

"And it will probably be accompanied by a revival — likely a loud revival — of the hawk-dove wars at the central bank."

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