Alaska Airlines revised its third-quarter profit down by 7. 9 percent because of a clerical error in accounting for a frequent-flier program. The revised net income is $61 million...

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Alaska Airlines revised its third-quarter profit down by 7.9 percent because of a clerical error in accounting for a frequent-flier program.

The revised net income is $61 million, down from $66.2 million reported in October, the carrier said in a Securities and Exchange Commission filing yesterday. The error reduced third-quarter profit for its parent, Seattle-based Alaska Air Group, to $74 million from $79.2 million.

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Alaska Airlines mistakenly recorded revenue from partners in its frequent-flier program who offer bonus miles as an incentive to use their products, said Caroline Boren, an Alaska Air spokeswoman. The cash should be booked in future quarters when the flights are taken, she said, not when the mileage is awarded.

“We elected to promptly inform investors” rather than record the adjustment in the fourth quarter, Boren said.

Alaska Airlines discovered the “clerical error” in its calculation this month, the filing said. The find resulted in an $8.4 million pretax drop in revenue for the third quarter and nine months ended Sept. 30, the filing said.

Profit for the nine-month period was revised to $23.9 million from $29.1 million at Alaska Airlines, the carrier said. Nine-month profit for Alaska Air Group fell to $29.6 million from $34.8 million.

Alaska Air Group’s third quarter was its first profitable quarter after three consecutive quarterly losses. Alaska Airlines, which serves cities along the Pacific Coast from Mexico to Canada, has accounted for about 80 percent of the parent’s operating revenue this year.

The other unit, Horizon Air Industries, is a smaller regional airline.

Alaska Air Group’s stock fell 22 cents to close at $32.08 yesterday.