BEAN is a newly proposed lightweight stream cipher adopting Fibonacci FCSRs. It is designed for very constrained environments and aims at providing a balance between security, efficiency and cost. A weakness in BEAN was first found by Ågren and Hell in 2011, resulting in a key recovery attack slightly better than brute force. In this paper, we present new correlations between state and keystream with large statistical advantage, leading to a much more efficient key recovery attack. The time and data complexities of this attack are 2^57.53 and 2^59.94, respectively. Moreover, two new output functions are provided as alternatives, which are more efficent than the function used in BEAN and are immune to all attacks proposed on the cipher. Also, suggestions for improving the FCSRs are given.