In this paper,we provide a unified expression to obtain the conditions on the restricted isometry constantδ2s(Φ).These conditions cover the important results proposed by Candes et al.and each of them is a sufficient condition for sparse signal recovery.In the noiseless case,whenδ2s(Φ)satisfies any one of these conditions,the s-sparse signal can be exactly recovered via(l1)constrained minimization. The this condition covers the significant results proposed by Candes et al. And each of them is a sufficient condition for sparse signal recovery. In the noiseless case, when δ2s (Φ) satisfies any one of these conditions, the s-sparse signal can be more accurately recovered via (l1) constrained minimization.