Correlation power analysis (CPA) is a well-known attack against cryptographic modules with which an attacker evaluates the correlation between the power consumption and the sensitive data candidates calculated from a guessed sub-key and known data such as plaintexts and ciphertexts. This paper enhances CPA to propose a new general power analysis, built-in determined sub-key CPA (BS-CPA), which finds a new sub-key by using the previously determined sub-keys recursively to compute the sensitive data candidates and to increase the signal-to-noise ratio in its analysis. BS-CPA also reuses the power traces in the repetitions of finding sub-keys to decrease the total number of the required traces for determining the all sub-keys. BS-CPA is powerful and effective when the multiple sensitive data blocks such as sbox outputs are processed simultaneously as in the hardware implementation. We apply BS-CPA to the power traces provided at the DPA contest and succeed in finding a DES key using fewer traces than the original CPA does.