Many algorithms for compressed sensing are studied. The common guarantee for the reconstruction algorithm is restricted isometry property (RIP), which is shown to only hold under ideal assumptions. However, in practice, more than one ideal condition is often violated and there is no RIP-based guarantee application. Based on this discrepancy, we propose a new oblique subspace thresholding pursuit (ObSTP) algorithm. It is guaranteed by the restricted biorthogonality property (RBOP) which requires no ideal assumptions.