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In this study, we define the identity of the singer with two independent concepts - timbre and singing style - and propose a multi-singer singing synthesis system that can model them separately. To this end, we extend our single-singer model into a multi-singer model in the following ways: first, we design a singer identity encoder that can adequately reflect the identity of a singer. Second, we use encoded singer identity to condition the two independent decoders that model timbre and singing style, respectively. Through a user study with the listening tests, we experimentally verify that the proposed framework is capable of generating a natural singing voice of high quality while independently controlling the timbre and singing style. Also, by using the method of changing singing styles while fixing the timbre, we suggest that our proposed network can produce a more expressive singing voice.