We propose a new type of guess-and-determine attack on the self-shrinking generator (SSG). The inherent flexibility of the new attack enables us to deal with different attack conditions and requirements smoothly. For the SSG with a length L LFSR of arbitrary form, our attack can reliably restore the initial state with time complexity O(20.556L ), memory complexity O(L2 ) from O(20.161L )-bit keystream for L 100 and time complexity O(20.571L ), memory complexity O(L2 ) from O(20.194L )-bit keystream for L < 100. Therefore, our attack is better than all the previously known attacks on the SSG and especially, it compares favorably with the time/memory/data tradeoff attack which typically has time complexity O(20.5L ), memory complexity O(20.5L ) and data complexity O(20.25L )-bit keystream after a pre-computation phase of complexity O(20.75L ). It is well-known that one of the open research problems in stream ciphers specified by the European STORK (Strategic Roadmap for Crypto) proje...