Reactive synthesis is the task of automatically deriving a correct implementation from a specification. It is a promising technique for the development of verified programs and hardware. Despite recent ad- advances in terms of algorithms and tools, however, re-active synthesis is still not practical when the specified systems reach a certain bound in size and complexity. In this paper, we present a sound and complete modular synthesis algorithm that automatically decomposes the specification into smaller subspecifications. For them, independent synthesis tasks are performed, significantly reducing the complexity of the individual tasks. Our decomposition algorithm guarantees that the subspecifications are independent in the sense that completely separate synthesis tasks can be performed for them. Moreover, the composition of the resulting implementations is guaranteed to satisfy the original specification. Our algorithm is a preprocessing technique that can be applied to a wide range of synthesis tools. We evaluate our approach with state-of-the-art synthesis tools on established benchmarks: the runtime decreases significantly when synthesizing implementations modularly.