It's possible there is some grit embedded in the pad. Take off the wheel and feel the pad for anything you might be able to remove. Then use sandpaper on the pad. If that doesn't change anything, it might be a toe-in issue. The pads should hit the rims either perfectly flat or with the front edge slightly ahead of the rear. If the rear edge hits first, they will squeal. If the pads aren't aligned properly, take an 8 inch crescent wrench (I'm assuming these are road brakes, not cantilevers) and snug it up on the flat of the brake caliper, just above or below the pad. Bend the caliper gently until the pad is flat or slightly toed in. Also check that the brake is firmly attached to the bike and there is no play between the caliper arms that could lead to vibration.
Lots of brakes squeal, some brands worse than others and some pad compounds worse than others. Some will squeal no matter what you do (if you had Mafac brakes in 1975, you had to live with it, but you didn't need a horn on the bike). Since these brakes didn't squeal when you got the bike, hopefully the squeak is correctable.