Though the sale of Eastern Airlines seems to promise major improvements, it's still too soon for the public to start cheering despite the joy with which the firm's strikers are greeting the move.

The strikers are especially elated at the prospective departure of Eastern owner Frank Lorenzo, whose reputation as a union-buster promised a long future of morale problems if he had managed to remain at the controls.Though the $464 million deal involves $210 million in union concessions, their impact is softened by the provision giving employees a 30 per-cent share in Eastern. What a heady experience it must be for these employees to suddenly find themselves part owners of the firm they have been striking against.

This deal also avoids the prospect of Eastern, the nation's seventh largest airline, getting carved up into a number of smaller carriers.

Moreover, new owner Peter Ueberroth - former baseball commissioner and organizer of the 1984 Olympics - brings to Eastern an enviable reputation as a no-nonsense manager and financial wizard responsible for turning around ailing enterprises.

But it's hard to envy him the challenges he now faces at Eastern. The firm, which is in bankruptcy, lost an estimated $626 million through the end of last year. While no current figures are available, it is thought to have lost over $100 million so far this year.

Though the sale could get the grounded airline back in the skies within days, it's also a complex deal, which still must be approved by the courts and whose fine print needs to be scrutinized closely.

Moreover, though Eastern enjoys a desirable route structure, industry analysts note it also suffers from a reputation for poor service. The new sale indicates that Ueberroth knows how to win over Eastern's employees. But his biggest challenge will be to win over air travelers.