We study a natural probabilistic model for motif discovery that has been used to experimentally test the effectiveness of motif discovery programs. In this model, there are k background sequences, and each character in a background sequence is a random character from an alphabet ∑ A motif G = g 1g2 ⋯ gm is a string of m characters. Each background sequence is implanted a probabilistically generated approximate copy of G. For a probabilistically generated approximate copy b1b 2 ⋯ bm of G, every character is probabilistically generated such that the probability for bi ≠ gi is at most a. It has been conjectured that multiple background sequences can help with finding faint motifs G. In this paper, we develop an efficient algorithm that can discover a hidden motif from a set of sequences for any alphabet ∑ with |∑| ≥ 2 and is applicable to DNA motif discovery. We prove that for a ≤ 1/4 (1 - 1|∑|) and any constant x ≥ 8, there exist positive constants c0, ε, δ1 and δ2 such that if the length ρ of motif G is at least δ1 log n, and there are k ≥ c0 log n input sequences, then in O(n 2+kn) time this algorithm finds the motif with probability at least 1- 1/2x for every G ε ∑ρ-ψ ρ,h,ε(∑), where ρ is the length of the motif, h is a parameter with ρ ≥ 4h ≥ δ2 log n, and ψρ,h,ε(∑) is a small subset of at most 2- θ(ε2h) fraction of the sequences in ∑ρ. The constants c0, ε, δ1 and d2 do not depend on x when x is a parameter of order O(log n). Our algorithm can take any number k sequences as input.