<p>Sparse signal recovery is one of the key problems in the field of compressive sensing. Restricted isometry property (RIP) is an important metric for the recoverability of sparse signals. It can provide explicit and simple sufficient conditions for the convergences of many reconstruction methods such as orthogonal matching pursuit, basis pursuit (BP), and hard thresholding pursuit. However, RIP has several drawbacks. One drawback is that RIP can not be preserved for the scalar rescaling. In order to overcome this drawback, a new metric named combinatorial condition number is defined in this paper. It is invariant for the scalar rescaling. Subsequently, the Wielandt inequality and robust null space property are utilized to present a sufficient condition for the sparse signal recovery by BP in terms of the new metric.</p>