We properly define off-shell K → π transition amplitudes and use them to extract information for on-shell K → ππ amplitudes within Chiral Perturbation Theory. At order p 2 in the chiral expansion all three parameters of weak interaction can be determined. At order p 4 we are able to fix eleven additional constants out of thirteen contributing to off-shell K → π transitions, which leaves four undetermined constants in the on-shell K → ππ amplitudes. All O(p 4 ) contributions have been exactly derived with m 2 π ≠ 0. We finally discuss the weak mass term issue and find contributions to on-shell ΔS = ± 1 kaon decays, in particular to transitions like K L → γγ, K L → μ + μ - and K S → π 0 γγ at the lowest non-zero order.