Let IK be a complete ultrametric algebraically closed field of characteristic 0. According to the p-adic Hayman conjecture, given a transcendental meromorphic function f in IK, for each n ∈ IN * , f n f takes every value b = 0 infinitely many times. It was proven by the second author for n ≥ 3. Here we prove it for n = 2 by using properties of meromorphic functions having finitely many multiple poles. .