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We show how to write any Kaehler metric of complex dimension 2 admitting aholomorphic isometry as a simple 1-real-function deformation of aGibbons-Hawking metric. Hyper-Kaehler metrics with a tri-holomorphic isometry(Gibbons-Hawking metrics) or with a mono-holomorphic isometry are recovered forparticular values of the additional function. The new general metric can beused as an Ansatz in several interesting physical problems.

On 2-dimensional Kaehler metrics with one holomorphic isometry