Group Key Agreement (GKA) allows multiple users to collaboratively compute a common secret key. Motivated by the very few existing GKA protocols based on secret sharing with formal security proofs, we propose a new method to build such protocols. We base our construction on secret n-sharing, an untraditional perspective of secret sharing that brings several advantages. Our proposal achieves better security than the existing work while it maintains a constant number of communication rounds regardless the group size.