We give a new protocol for reliable broadcast with improved communication complexity for long messages. Namely, to reliably broadcast a message m over an asynchronous network to a set of n parties, of which fewer than n/3 may be corrupt, our protocol achieves a communication complexity of \(1.5 |m | n + O( \kappa n^2 \log (n) )\) , where \(\kappa \)  is the output length of a collision-resistant hash function. This result improves on the previously best known bound for long messages of \(2 |m | n + O( \kappa n^2 \log (n) )\) .