(Fortune) -- Not so long ago, it would have been heresy to say Goldman Sachs should take a cue from Citigroup. But as Goldman's sins come to light, Lloyd Blankfein could do worse than to follow Vikram Pandit's path to redemption.
Goldman's giant pay packages and its omnipresent ties to Washington have made it a target for populist outrage since the financial crisis hit. That anger is now bubbling over following Securities and Exchange Commission allegations that Goldman ripped off some clients by aiding a hedge fund customer that profited from their misguided bets.
Goldman denies the charges. But even some who take the firm's side say big changes are overdue. They start with the composition of Goldman's board and the tone of the firm's dealings with the public -- two areas in which Citi (C, Fortune 500) has made real strides.
"Goldman has taken a real drubbing in the court of public opinion," said Eric Jackson, an activist investor and hedge fund manager in Naples, Fla. "That is a perfect reason for making some changes."
Jackson has been saying since last year that Goldman's board is too cozy and lacking in financial know-how to diligently oversee top management.
The problem with these choices, Jackson said, is that "these people seem to be favorably disposed to senior management's way of thinking," and are therefore unlikely to act as a check on CEO Lloyd Blankfein and his team.
Coziness isn't the only strike against Goldman's board, Jackson said. He believes it is also lacking in financial savvy. Where Citi has reshuffled its board to add the likes of former U.S. Bancorp (USB, Fortune 500) chief Jerry Grundhofer and onetime Philadelphia Fed President Anthony Santomero, Goldman's board lacks any bank CEOs or former top regulators.
And then there are the scandals.
Regulators are examining the role of Rajat Gupta, who said last month he won't return to Goldman's board, in the Galleon insider trading case. Stephen Friedman, who remains on Goldman's board, quit the New York Fed after he was found trading Goldman stock, which is a no-no.
"The board is becoming a lightning rod," said Eleanor Bloxham, who runs the Corporate Governance Alliance in Westerville, Ohio. "Lightning keeps striking them over and over."
All of this has added up to a significant blow to Goldman's once glowing reputation.
"I don't know who's been giving Goldman advice about their public relations, but it has been a disaster," said Jackson, who has no stake in Goldman but owns shares of Citi. "They need to get ahead of this train."
Pandit, after his bank's many brushes with disaster, has recently tried to make amends. Citi's board has added eight members over the past year and the bank lately has been emphasizing its gratitude for taxpayer support extended in the dark days of 2008-2009.
"We owe taxpayers a huge debt of gratitude for assisting us at a critical time," Pandit said in Citi's earnings release Monday.
Of course, Pandit has an easier task than Blankfein in the sense that Citi's governance couldn't get worse than it did in the bubble days. Back then, the firm ended up loaded with toxic investments and prominent board members professed total ignorance.
Still, Goldman has been all over the map. Blankfein issued a vague apology late last year for the bank's role in the subprime crisis, not long before he infamously told a British newspaper Goldman was doing "God's work."
And though Goldman has highlighted its support of pay reform measures such as clawbacks and bans on guaranteed bonuses, in one way its corporate governance is behind the times. Blankfein continues to serve as chairman and CEO, even as the trend in recent years has been toward independent board leadership.
At a time when every decision at the firm is going to come under scrutiny, that conflict doesn't look like a winner in the eyes of the public.
"The issue for Goldman directors is whether they have been able to control the agenda," said Bloxham. "Directors must be asking, can we do our job?"