The purpose of this paper is to construct certain canonical bases in irreducible finite dimensional representations of \(G=Sp(4,{\mathbb{C}})\). Let \(N_-\) be a unipotent radical of G, \(A=N_-\setminus G\) the affine base space of G, and \({\mathbb{C}}[A]\) its coordinate ring. Each irreducible G- module appears in the decomposition of \({\mathbb{C}}[A]\) precisely once. The vectors in the canonical bases are certain highly symmetric monomials on A. This result is an extension to the case of \(G=Sp(4,{\mathbb{C}})\) of results of I. M. Gel’fand and the first author on existence of canonical bases for \(Gl_ n\) [see in particular Funkts. Anal. Prilozh. 19, No.2, 72-75 (1985; Zbl 0606.17006)]. As the authors show in the last section, the existence of canonical bases sheds a light on the problem of decomposition of a tensor product of two irreducible G-modules into a direct sum of irreducible modules.