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Special spin-transfer-driven magnetic behaviors can take place in a spin valve nanopillar with perpendicular anisotropy due to reduced symmetry of easy axis. Micromagnetic simulation demonstrates a dip in the average magnetization curve, which corresponds to the experimentally observed undulation of dc resistance. The dip is a signature of spin-transfer-driven reversable magnetic process with slightly tilted easy axis in the free layer. This featured magnetization dynamics includes non-uniform magnetization precession and multi-mode propagating spin waves, which are attributed to the competition among tilted magnetic anisotropy, magnetic field, and spin transfer torque.