We prove that the multipole Lempert function is monotone under inclusion of pole sets.Let D be a domain in C n and let A = (a j ) l j=1 , 1 ≤ l ≤ ∞, be a countable (i.e. l = ∞) or a non-empty finite subset of D (i.e. l ∈ N). Moreover, fix a function p :p is called a pole function for A on D and |p| its pole set. In case that B ⊂ A is a non-empty subset we put p B := p on B and p B := 0 on D \ B. p B is a pole function for B.For z ∈ D we set 2000 Mathematics Subject Classification. Primary:32F45.