Two communities can burn their trash more efficiently than one.

With that logic the Alexandria City Council voted early yesterday to take the first step toward creation of what could become a multimillion-dollar facility that would transform trash from several jurisdictions into steam and electricity that could be sold for profit.

The council voted unanimously to begin negotiations next month to sell its Eisenhower Avenue trash facility to a private contractor, Clark-Kennith Inc., which would build a $45 million "waste-to-energy" facility.

"It looks like a win-win situation," said Arlington County Board Charman Ellen M. Bozman yesterday. "It's better for Alexandria and us to choose a combined facility."

Arlington, which has been eagerly awaiting Alexandria's decision as a possible solution to its own trash problems, is expected to approve the county's participation in the project at its Sept. 24 meeting.

Arlington's incinerator, in Crystal City, was shut down years ago for violating state and federal air pollution standards, but the plant is used as a transfer station where trash is compacted before being trucked to the Lorton landfill in Fairfax County.

The Virginia health department has been pressing Arlington to do something about refuse spillover at the plant, and residents have been complaining it is a smelly eyesore. Arlington has been considering building a new waste facility at the Crystal City site, joining with Alexandria or Fairfax County in a similar project, or finding a new landfill.

Dayton L. Cook, Alexandria's director of transportation and environmental services, said special state antitrust legislation will be needed before the communities can operate the plant since they will have to guarantee a certain amount of trash to a private firm for a 20-year period. Plans for the plant call for an average 270 tons daily from Alexandria and 430 from Arlington once the facility is open. That could be as early as 1986.

Cook said the city stands to save more than $1 million annually, much of it in transportation costs. It will pick up a minimum of $400,000 annually from having the facility under private ownership.

"This would be a great improvement for South Arlington," said Michael Hall, president of the Arlington Ridge Civic Association, which has been fighting proposals for a new facility in their area.

"We could get rid of the transfer station and the possibility of an incinerator. We can't be anything but happy," added Hall. The neighborhood has complained about several other public facilities in the area, including a water-treatment plant, railroad yards, a power company substation, highrise buildings and National Airport.

Should the Arlington-Alexandria project collapse, Arlington County Manager Larry J. Brown said the county will be "back in contact" with Fairfax County about joining a new trash facility Fairfax is planning. Andrew H. Quigley, an engineer with Fairfax's solid waste divison, said, however, the county's plans are not contingent on participation from Arlington and Alexandria.