Angular variation in giant magnetoresistance and spin-transfer torque in metallic spin-valve heterostructures is analyzed theoretically in the limit of diffusive transport. It is shown that the spin-transfer torque in asymmetric spin valves can vanish in noncollinear magnetic configurations, and such a nonstandard behavior of the torque is generally associated with a nonmonotonic angular dependence of the giant magnetoresistance, with a global minimum at a noncollinear magnetic configuration.