Coach Sam Wyche, whose job reportedly was in jeopardy after his team's 4-11 season, will be back for the fifth and final year of his contract in 1988, the team announced yesterday.

"We've decided that we'll honor the fifth year of Sam's contract. He will be the coach next season," said General Manager Paul Brown, founder of the 19-year-old franchise.

The Bengals, 10-6 in 1986, ended their season Sunday by losing, 21-17, to the Houston Oilers and finishing last in the four-team AFC Central Division. The 4-11 record was the third-worst mark in the Bengals' history.

Wyche, 42, who was hired four years ago Monday, is due to earn about $250,000 in 1988. He has failed to take the Bengals to the NFL playoffs in his four seasons as coach.. . .

Quarterback David Archer, kick return specialist Billy (White Shoes) Johnson, wide receiver Charlie Brown and linebacker Reggie Wilkes were cut by the Atlanta Falcons. . . .

Cleveland Browns nose tackle Bob Golic underwent surgery on his broken right arm and will not likely recuperate in time to play in either the Super Bowl or the Pro Bowl, the team reported.

Team physician John Bergfeld said the surgery went well and a complete mending of the injury was anticipated, according to team spokesman Kevin Byrne. However, Bergfeld described it as a "full six-week injury," Byrne said.