Blankfein saw his own time as CEO as a privilege and says a CEO has a special obligation to others. "You always have to remind yourself what you owe to the people who support you in this privileged position."

David Solomon is currently celebrating his first week as CEO of Goldman Sachs and his predecessor Lloyd Blankfein has some simple advice that can help any leader: "Never think about what you're owed," he says in a one-on-one conversation released Monday. Blankfein tells Solomon, "Always think about what you owe someone else."

The former Goldman Sachs CEO says he realized people were only ever interested in what he said or posted online because of his role. "I was conscious that the platform that gives me the voice and the leverage I have is a platform that really belongs to the firm and the constituents of the firm," says Blankfein.

Both executives have spent the better part of their careers working for Goldman Sachs — Blankfein had been CEO for the past 12 years. Solomon's appointment comes several months after the company tapped him to be its sole president and chief operating officer.

The ex-CEO is confident Solomon's start will go smoothly.

"You're so much more equipped and organized than I was," says Blankfein.

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