This paper establishes a high order condition on the restricted isometry property adapted to a frame D (D-RIF) for the signal recovery. It is shown that if the measurementmatrix A satisfies the D-RIP condition δtk 〈t-1/t for t 〉 1, then all signals f which aresparse in terms of a tight frame D can be recovered stably or exactly via the l1-analysis model based on y= Af + z in 12 and Dantzig selector bounded noise setting.