Last week, hedge funds PAR Capital Management and Altimeter Capital Management teamed up to mount an activist challenge to the board of United Continental (UAL -1.25%).

The two funds, which together own 7.1% of United's stock, are frustrated with the airline's poor financial performance relative to peers. As a result, they are nominating six candidates for the board, led by former Continental Airlines CEO Gordon Bethune, who would become United's executive chairman.

Activist investors are attempting to reshape United Continental's board.

It's true that United has underperformed for many years. However, the company has made some wise strategic choices in the past year and has a new CEO in place who has laid out a promising (though unproven) turnaround strategy. This is not the right time for investors to back an activist campaign that could disrupt United Continental's progress.

New CEO, new strategy
Six months ago, United Continental CEO Jeff Smisek resigned in the midst of a corruption investigation. He was replaced by Oscar Munoz, a longtime CSX executive who had joined Continental Airlines' board in 2004 and remained on the board following the merger with United.

Oscar Munoz has catalyzed a huge improvement in labor relations. Image source: United Continental.

In his first few weeks as CEO, Munoz devoted a lot of time to meeting front-line employees. His fresh approach sparked a huge improvement in labor-management relations compared to the toxic environment he inherited. However, Munoz suffered a heart attack little more than a month after he took the top job.

Even though Munoz had only been CEO for a short time when he went on medical leave, it quickly became clear that his lieutenants were buying in to United's new strategy.

First, United made progress on the labor front. Earlier this year, its pilots ratified a contract extension and its flight dispatchers ratified a new contract. United also reached a tentative agreement with its mechanics' labor union, although that accord was voted down by the membership.

Second, United Continental has taken steps to improve its reputation with customers. The carrier has brought back free snacks in economy class and it is upgrading the quality of its coffee. United is also building on its strong position in Asia by launching a handful of new routes to cities that don't have any nonstop flights to the U.S. today.

This week, Munoz finally returned to work on a full-time basis. On his first full day, he held a summit with top leaders from United's labor unions. Most of the labor leaders seemed pleased with how the meeting went.

Munoz still needs to show that he can capitalize on higher employee engagement to improve reliability and customer service, win back key corporate clients, and -- ultimately -- boost unit revenue. That will take time. But at least he has United on a promising path.

The case for a new board
For the most part, PAR and Altimeter have directed their criticism at United's board, not at the CEO. (However, they do oppose United's plan to make Munoz chairman of the company next year, rather than having an independent chairman.)

The hedge funds have chastised the board for its slow response as United's position in the airline industry deteriorated in recent years. PAR and Altimeter also note that most of the board members lack airline industry experience. While United recently appointed three new board members (two of whom have worked in the airline industry), the funds see this move as too little, too late.

United's activist challengers blame the board for the company's problems.

Indeed, two years ago, I criticized United Continental's management for making excuses about the company's poor results rather than fixing the underlying problems. United's board should have brought in new management then.

Instead, it gave former CEO Smisek more leeway than he deserved. Given that Smisek also served as chairman at the time, it appears that the board wasn't sufficiently active and independent of management to guide the company effectively.

Why I won't be supporting the activists
Nevertheless, as a United Continental shareholder, I plan to support the company (and the board) against the current activist challenge. Two years ago, United needed new leadership, but that's not the case today. United has a lot of work ahead to get its performance back up to par, but it appears to be making the right moves to get there.

Even though PAR and Altimeter would keep Munoz on as CEO, he would essentially be getting a new boss if Gordon Bethune becomes chairman. That could lead to more strategy changes or delayed implementation of Munoz's strategic initiatives, slowing United's turnaround progress.

Furthermore, Munoz has done a remarkable job of winning support from labor leaders in a short period of time. Several union leaders have vocally expressed their support for his leadership. Just a year ago, investors would have settled for mere detente between the company and its unions.

Many of those same labor leaders are concerned about the hedge funds' proxy campaign. A setback in labor relations would be a huge blow to the company -- and it might not be so easy to win back labor's trust a second time. If Munoz can't deliver results in the next couple of years, another shakeup might be in order. But for now, United Continental shareholders should stay the course.