In Cryptography, group key distribution protocol is a mechanism in which a group key is generated and distributed by Key Generation Centre (KGC) to a set of communicating parties in a group. This group key generally ensures secure communication among communicating parties on an insecure channel. Key establishment protocols allow two or more communicating parties to establish their common secret key called a session key. Harn and Lin protocol (HL) is one such protocol and it is based on Shamir's threshold secret setting. Nam et al. exposed the vulnerability in HL protocol through their replay attack and proposed a countermeasure using a nonce mechanism. In this paper, we are general-izing the replay attack presented by Nam et al. and proposing an alterna-tive countermeasure without using nonce mechanism. The novelty of our countermeasure is that KGC is not required to detect replay messages and hence each user doesn't need to compute authentication messages as in Nam et al. Presented countermeasure thereby brings down the computational complexity of the scheme. Also, we propose an improved version of HL protocol a version that uses short signatures for authentication and overcomes drawbacks, and is resistant to existing attacks.