In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um + γup = 0,where γ≥0, m＞ 1 and p＞m+2/N. We will show that if γ = 0 and 0 ＜μ＜ 2N/N(m-1)+2,or γ＞0 and 1/p-1＜μ＜2N/N(m-1)+2,then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space 5(RN), there exists an initial-value uo ∈ C(RN)with limx→∞ uo(x) = 0 such that φ is an ω-limit point of the rescaled solutions t μ/2 u(tβ.,t),where β=2-μ(m-1)/4.