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Power analysis poses a significant threat to the security of cryptographic algorithms, as it can be leveraged to recover secret keys. While various software-based countermeasures exist to mitigate this non-invasive attack, they often involve a trade-off between time and space constraints. Techniques such as masking and shuffling, while effective, can noticeably impact execution speed and rely heavily on run-time random number generators. On the contrary, internally encoded implementations of block ciphers offer an alternative approach that does not rely on run-time random sources, but it comes with the drawback of requiring substantial memory space to accommodate lookup tables. Internal encoding, commonly employed in white-box cryptography, suffers from a significant security limitation as it does not effectively protect the secret key against statistical analysis. To overcome this weakness, this paper introduces a secure internal encoding method for an AES implementation. By addressing the root cause of vulnerabilities found in previous encoding methods, we propose a balanced encoding technique that aims to minimize the problematic correlation with key-dependent intermediate values. We analyze the potential weaknesses associated with the balanced encoding and present a method that utilizes complementary sets of lookup tables. In this approach, the size of the lookup tables is approximately 512KB, and the number of table lookups is 1,024. This is comparable to the table size of non-protected white-box AES-128 implementations, while requiring only half the number of lookups. By adopting this method, our aim is to introduce a non-masking technique that mitigates the vulnerability to statistical analysis present in current internally-encoded AES implementations.