Apple CEO Tim Cook speaks after the new iPad mini unveiling during an Apple special event at the historic California Theater on October 23, 2012 in San Jose, California. (Kevork Djansezian/GETTY IMAGES)

When Tim Cook took over Apple following Steve Jobs’ death, many wondered what kind of leader he would be. We knew he was strong at executing on the operations behind Jobs’ technology and design brilliance. We knew he had been an able and competent manager who’d earned the respect of Wall Street during Jobs’ health absences. And since taking over the company, we’ve learned that he’s willing to do things Jobs was against, such as making investors and employees happy with stock-buyback and charitable-giving programs.

But on Monday, with the announcement of a surprise management shake-up, we got an even better picture of what kind of leader Cook will be: one who isn’t too proud to admit his mistakes, and expects his team to be willing to do the same.

First, reports about the departure of software executive Scott Forstall, who managed the company’s mobile operating system, demonstrate Cook’s focus on creating a team that doesn’t tolerate outsized egos and remains willing to apologize when it messes up. The final straw in Forstall’s exit was reportedly his refusal to sign a public apology over the company’s flawed maps software in the iPhone 5 release. But even before that, as the Wall Street Journal reported Monday, Forstall apparently had the reputation among senior executives at Apple for not being cooperative and for showing off his close relationship with Apple’s late co-founder Steve Jobs. Forstall’s duties will be taken over in part by senior vice president Craig Federighi, who is described as more “even-keeled.”

The second thing Monday’s shake-up tells us is that Cook is not afraid to admit he was wrong. Also departing the company will be Apple stores head John Browett, who was known for bringing in cost-cutting measures and implementing a store-hours scheduling formula that cut employees’ hours. Browett started just six months ago, after Cook became CEO, but reports say he was not a fit with the company’s culture. It’s often said that one of the biggest blunders leaders make is not being willing to cut cultural misfits they’ve hired soon enough. Cook shows little danger of falling prey to this mistake.

Finally, the news tells us that Cook is willing to take ownership of errors made by the company, even when he could have blamed it on his deputies. Reports say that when Forstall refused to sign the public apology over the maps software, Cook did so instead. He could have dropped Forstall in that moment and blamed the problems on Forstall’s team. He didn’t, choosing to take the heat personally for the problem and to shake up his staff weeks later.

Apple’s stock may have dropped from its staggering price in recent weeks. Some may question the company’s pricing for its iPad mini, which follows its competitors on size. But what Monday’s shake-up says to me about Tim Cook’s leadership—that he is someone who values even-keeled executives and a humble approach to running the company—should be very comforting to anyone worried about who’s steering the ship.

Jena McGregor is a columnist for the Washington Post’s On Leadership section.

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