Multi-server authentication enables the subscribers to enjoy an assortment of services from various service providers based on a single registration from any registration centre. Previously, a subscriber had to register from each service provider individually to avail respective services relying on single server authentication. In the past, a number of multi-server authentication techniques can be witnessed that employed lightweight and even computationally intensive cryptographic operations. In line with this, Zhu has presented a chaotic map based multi-server authentication scheme recently, which is not only vulnerable to denial-of-service attack, stolen-verifier attack, but also lacks anonymity. This research aims at improving the Zhu's protocol in terms of cost and efficiency. Moreover, the comparative study is presented for the performance of improved model against the existing scheme, and the security of proposed model is formally proved using BAN Logic.