Vice President Dan Quayle cancelled a second round of golf at a California course today after being criticized for playing at the country club with an all-white membership. His office said he had been unaware of the controversy surrounding the Cypress Point Club. Quayle shot more than 18 holes Thursday at the course in Pebble Beach. Beach. The Professional Golfers Association in September ruled the club ineligible for the 1991 AT&T Pebble Beach National Pro-Am. ``I have a great concern about the vice president of the United States playing at Cypress Point and not being aware of the sensitivity of the issue that revolves around it,'' Monterrey County Supervisor Sam Karas said. Quayle couldn't be questioned for reaction because Secret Service agents kept reporters and photographers off the club's private grounds. But his office in Washington released a statement from Press Secretary David Beckwith, stating Quayle was ``unaware of the controversy surrounding the Cypress Point golf course. He has been assured the club does not discriminate and has never had a policy of discrimination.'' However, the statement said, ``The vice president is unwilling to leave any impression that he condones any form of discrimination. He has therefore canceled his round of golf today.'' Quayle is a member of the Burning Tree country club outside Washington, which has an all-male membership. He was returning to his skiing vacation in Colorado before returning to Washington on Saturday. Quayle will leave Saturday night for a New Year's visit to the troops in the Persian Gulf. Asked how Quayle could be unaware of the highly publicized controversy involving the club's banning from the national tournament, his chief of staff Bill Kristol said in a telephone interview: ``It proves he's not spending time reading the golf pages.'' An official who answered the telephone at the club's hotel, where Quayle was staying, said the staff had been instructed not to try to contact Quayle's party. Golfing with Quayle on Thursday were two Cypress Point Club members who are prominent officials in the Bush administration - Donald B. Rice, the Air Force secretary, and Ebersole Gaines, U.S. Ambasador to the Bahamas.