CHICAGO — United Airlines embarked Wednesday on what it called “a new beginning,” soaring free of bankruptcy for the first time since 2002 but no longer able to turn to a court for assistance as it faces industry conditions that may be harsher than those when it entered 38 months ago.

The end of Chapter 11 for United and parent UAL Corp. came with the filing of exit documents in U.S. Bankruptcy Court, climaxing the longest and costliest airline restructuring in history.

The next chapter of its recovery won’t be easy, either, with the slimmed-down carrier having to overcome near-record oil prices and multiple discount competitors if it is to succeed and make its first profit since 2000.

Several of United’s unions, still stinging from steep pay cuts and other concessions in bankruptcy, issued statements putting management on notice that they expect to see better results for all their sacrifices. “With bankruptcy behind us, there are no more excuses, no room for error and no second chances,” said Mark Bathurst, head of the pilots’ union.

The departure from bankruptcy after 1,150 days, however, mostly was cause for quiet celebration within the nation’s second-largest airline — and some subtle rebukes for critics who said cost-laden United couldn’t pull off the wholesale restructuring.

“When we started this journey three years ago, many people questioned our ability to rebuild United into a company with a sustainable future,” CEO Glenn Tilton said in a message to employees. “But together we have created a fundamentally better airline — strong, confident and ready to compete with the world’s best.”

Top executives of the Elk Grove Village, Ill.-based carrier fanned out to U.S. airports to thank United’s employees for their sacrifices and customers for their loyalty and patience.

“It’s a new beginning,” said Pete McDonald, chief operating officer, as he began a round of handshakes and chats with upbeat employees at Chicago’s O’Hare International Airport before boarding a flight to do the same thing in San Francisco.

“We’re very thankful to our employees for their contributions and their focus on our customers, and we’re very thankful to our customers for sticking with us through this difficult time,” he said.

Passengers likely did not notice any difference Wednesday, since United never stopped flying even when multibillion-dollar losses forced it to seek protection from its creditors in federal bankruptcy court. But the airline has made one change after another since early in its overhaul.

It now has about 30 percent fewer employees (58,000), 20 percent fewer airplanes (460) and 20 percent lower operating costs (7.5 cents per seat per mile), excluding fuel, than it did when the bankruptcy began on Dec. 9, 2002. Labor costs are down by more than $3 billion annually after two steep pay cuts and the elimination of defined-benefit pensions. Dozens of daily domestic flights have been eliminated.

Some things are up, too, including the number of international routes, on-time arrivals, the percentage of seats filled and the cost of on-board meals, no longer free to all.

Bucking the cheaper-is-better trend, United also has added or expanded products targeting both ends of the price spectrum. Besides its two-year-old discount airline Ted for leisure travelers, it has an enlarged Economy Plus program with extra leg room for frequent or higher-paying travelers and a premium transcontinental service called “p.s.” offering more comfort for more money.

All told, United shed $7 billion in annual expenditures during the complex makeover.