Attribute-Based Encryption (ABE) is a cryptographic primitive which supports fine-grained access control on encrypted data, making it an appealing building block for many applications. Multi- Authority Attribute-Based Encryption (MA-ABE) is a generalization of ABE where the central au- thority is distributed across several independent parties. We provide the first MA-ABE scheme from asymmetric prime-order pairings where no trusted setup is needed and where the attribute universe of each authority is unbounded. Moreover, it is the first to handle non-monotonic access structures. These features broaden the applicability and improve the efficiency of our scheme. Our construction makes a modular use of Functional Encryption schemes with fine-grained access control.