Let n ≥ 3 and let ψλ0 be the radially symmetric solution of Δ log ψ + 2βψ + βx · ∇ψ = 0 in ℝn, ψ(0) = λ(0), for some constants λ0 > 0, β > 0. Suppose u0 ≥ 0 satisfies u0 − ψλ0 ∈ L1 (ℝn) and u0 (x) ≈ (2(n − 2)/β)(log∣x∣/∣x∣2) as ∣x∣ → ∞. We prove that the rescaled solution ũ(x,t) = e2βtu(eβtx, t) of the maximal global solution u of the equation ut = Δ log u in ℝn × (0, ∞), u(x, 0) = u0 (x) in ℝn, converges uniformly on every compact subset of ℝn and in L1 (ℝn) to ψλ0 as t → ∞. Moreover, ∥ũ(·, t) − ψλ0∥L1(ℝn) ≤ e−(n−2)βt∥u0 − ψλ0∥L1(ℝn) for all t ≥ 0.