The second biggest airline is by far the most puzzling.

Alone among the 10 largest carriers, United ( UAUA) has neither placed a major aircraft order recently nor expressed any interest in doing so. Instead, it seems singularly focused on finding a merger partner. The search has led nowhere -- not surprisingly, given that airline mergers rarely succeed.

Meanwhile, United's financial performance has been, to quote Winston Churchill, "a riddle, wrapped in a mystery, inside an enigma." Since it emerged from bankruptcy in February 2006, United has ridden a financial roller coaster. Its fortunes decline one minute, as they did in the first quarter, then rise the next, as they did last week.

Although it operates an imposing global route system at a time when international routes far outperform domestic ones, United sometimes appears to be floundering. "No analyst out there can figure out why they are not doing a better job," said aviation consultant Robert Mann. "This ought to be a gold mine."

Instead, United is viewed as having failed to get all it needed from a bankruptcy that consumed three years. By contrast, Delta ( DAL) spent 20 months in bankruptcy, yet remade itself. And United is often compared to American ( AMR), which has similar costs despite not entering bankruptcy at all.

United CEO Glenn Tilton came to the airline business with an outsider's perspective. Before joining United in 2002, he spent 32 years at Texaco, overseeing a 2001 merger with Chevron. Now, after less than four years in an insular industry staffed largely by lifers who are in love with it, he sometimes seems to tell airlines what to do.

To watch Brittany Umar's video take of this column, click here .

United service has deteriorated. In 2006, United tied US Airways ( LCC) for highest complaint volume among the 18 largest airlines, according to the Department of Transportation. Also in 2006, United showed the industry's biggest service decline, according to the University of Michigan's American Customer Satisfaction Index.

Many United employees are unhappy. Hundreds demonstrated outside the annual meeting last month. Inside, others challenged Tilton over what they see as excessive pay and understaffing.

To be sure, there has never been a shortage of people with bad things to say about United management. By many measures, the airline's most successful CEO was Stephen Wolf. Between 1987 and 1994, he presided over unprecedented international growth and ordered hundreds of new airplanes, including the first 777 jets produced by Boeing ( BA). Yet Wolf was forced out, largely because of conflict with the pilots union.

Two weeks ago at an investor conference, CFO Jake Brace -- a Wolf lieutenant hired him from American in 1988 -- spoke of United's intentions. He defined what United wants in a merger partner, primarily strength in the Northeast and the South. He also said the carrier will not order airplanes for the foreseeable future.

United's 94 Boeing 737 jets average 18 years of age. They would normally be replaced after 25 years, Brace said, so United can wait until Airbus and Boeing come up with something new.

"We've been encouraging them to launch a new generation narrowbody, to do what the 787 and the A350 will do for the widebody," Brace said. "Our interest is in replacing them with that technology, which doesn't currently exist." Forrester Research analyst Henry Harteveldt says United is stalling, "hoping they will be bought before the airplanes would be delivered."

As for financial results, United's first quarter disappointed. The company lost $152 million and missed analyst expectations, just as it had in the fourth quarter. Yet in the third quarter, United led the industry, earning $190 million and producing better margins than its peers.

Recently, the news has been good. United's May unit revenue growth apparently led the industry. Last week, it forecast second-quarter unit revenue will rise, while costs will decline.

Subsequently, Cathay Financial analyst Susan Donofrio raised her price target for United to $40 from $30, while maintaining a neutral rating. Donofrio said the company's EBITDAR margin -- or cash flow as a percentage of revenue -- lags peers. She expects United to report a 2007 EBITDAR margin of 11%. Meanwhile, American, Continental ( CAL) and Delta will likely report margins of 17%, 15% and 15% respectively. United closed Tuesday at $38.61.

Standard & Poor's assigns United a rating of B stable, below investment grade. That puts it in the middle of the top 10 airlines, equivalent to Continental and Delta, with four carriers higher and three lower.

It is revealing to compare United with its peers.

American CEO Gerard Arpey has 25 years at the company. During his career, American has been involved in mergers with AirCal, Reno and TWA. All three are generally felt to have been failures, producing headaches but no value.

Arpey won't talk specifically about mergers, but American appears to be reluctant, more focused on winning by out-managing its competitors. Its unique initiatives include cutting costs by flattening seasonal flying, rather than chasing summer revenue.

Delta CEO Gerard Grinstein has 23 years in the industry. That includes time on Delta's board, which he joined in 1987 after Delta acquired Western Airlines, where he was CEO. The deal is considered a rare example of a successful airline combination, but Grinstein is no fan of mergers, calling them last resorts that enable failing airlines to survive. He rebuffed a 2005 approach by Tilton.

While they have low interest in mergers, both American and Delta have a high interest in new airplanes. American is ordering 737s to begin to replace its 300 MD80s -- which consultant Scott Hamilton notes are about the same age as United's 737s -- and talking about 787 orders. Delta, meanwhile, says it will likely order about 125 widebody jets this year.

For Mann, the consultant, seeking a merger means United "is swinging for the fences." Perhaps, he suggested, it should "try to hit a few singles."

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