UAL ( UALAQ), the parent of United Airlines, announced a narrower but still-whopping first-quarter loss, despite a double-digit percentage increase in revenue.The carrier announced Thursday that its loss narrowed to $459 million, or $4.17 a share, from $1.34 billion, or $14.16 a share, a year earlier. On an operating basis, the loss narrowed to $211 million from $813 million a year ago. Because the company's shares are bankrupt, and will likely be worth nothing if and when the company emerges from bankruptcy, there are no earnings estimates for the company, which is no longer covered by analysts. Revenue came in at $3.73 billion, up 17.2% from the year-ago $3.18 billion, while expenses fell 1.4% to $3.94 billion. Fuel costs rose 5.6% in the quarter, helping offset an 18.7% drop in wages and a 31.8% drop in aircraft rent. "We are doing exactly what we said we would do to be able to succeed in the new revenue environment -- maintaining a relentless focus on reducing costs and improving efficiency," said Glenn Tilton, chairman, president and CEO. "But, there is still a lot of work ahead of us. Like the rest of the industry, we are impacted by fuel prices. Unlike our peers, though, we have landmark, consensual six-year labor agreements that will differentiate us competitively in the years ahead." While United's loss will likely be the largest posted by any airline in the first quarter, the carrier nonetheless saw some aspects of its business improve. The carrier's yield, a measure of the total amount of revenue it brings in per passenger, rose 9% in the quarter, one of the best yield improvements in the entire industry. Furthermore, the company said bookings for May and June were trending above last year's levels, despite the fact that it had added a number of flights.