As board president, Kline said he also will "have a little bit more say" than other board members.
In a separate vote, Byers was named vice president despite two dissenting votes from board members Edwin Hayes and Doris J. Nipps.
Nipps said she voted against Byers because she believed it was time for new leadership on the board, especially with a new superintendent.
"I'd just as soon not say anything else," Nipps said.
Byers declined to comment on the votes against her.
Byers has been a member of the Board of Education since 1970 and has served as president numerous times. Her longest term as president was from 1974 to 1977.
Kline is serving his fourth year as a board member and is planning to run for re-election next year. Five seats on the board will be on the ballot in 1998.
Board member Andrew R. Humphreys said during Tuesday's board meeting that it was a year ago today that he and Hayes were sworn into office. Humphreys thanked the voters who put him in office and he said his first year on the job has been "a challenging one and a wide-ranging one."
Board members earn $3,200 a year, and the president makes an extra $100. "So I'm not doing it for the pay," Kline said.
Byers said the board president acts like a manager of the board, handling correspondence and other duties.