New York Air, still playing David to Eastern's Goliath, this week announced a schedule change to lure passengers away from the popular shuttle between the Big Apple and the nation's capital.

Starting June 1, New York Air's planes will depart for Washington once an hour on the half hour from 7:30 a.m. to 8:30 p.m. Together, Eastern and New York Air will supply continuous shuttle service between the cities throughout the day.

New York Air is running advertisements this week telling passengers about the new flexibility. "You can literally choose your flight as you're approaching the airport," it reads. "For example, if it's before the half hour, head for New York Air. If it's after the half-hour, head for Eastern."

To facilitate this cozy operation, New York Air will provide free minibus service, named the Shuttle-Shuttle, to carry passengers once an hour between the two lines at LaGuardia. At National, passengers will have to walk.

Eastern passengers who board the LaGuardia bus will be assured of getting a seat on the next New York Air flight and may even buy their tickets on the bus. But customers in the other direction will not be assured of getting on the next Eastern shuttle.

As friendly as this arrangement appears, it is really a marketing move to win over Eastern passengers who would otherwise have to wait for another hour--or catch a specially scheduled back-up flight when available--to get out of New York. Travelers also can purchase their tickets on the plane.

"We invite Eastern to cooperate," quipped New York Air President Mike Levine. Eastern's reply: "We do not appreciate it. New York Air has changed gears many times, but it hasn't taken business away from us."

New York Air began in late 1980 as a low-fare, reserved-seat alternative to the Eastern shuttle. But it failed to make money, so it raised fares to equal Eastern's. And, like Eastern, it now accepts no-reservation passengers on a space-available basis and allows them pay on board. It decided to switch to a half-hour departure from New York after it found that it was carrying more people on its northbound flights, which leave on the half hour, than on its hourly flights southbound.

Levine was asked if New York Air, unable to beat Eastern, had decided to join it. He replied, "We offer a different service. We concluded that we could still offer amenities--confirmed reservations and free newspapers and drinks--while offering convenience." He added that New York Air is now running solidly in the black but declined to give any figures on passenger loads.