In the realm of video coding, the quest for enhanced efficiency is unending. This study introduces a novel optimization in High Efficiency Video Coding (HEVC) by refining intra-mode estimation through Hadamard cost analysis. With the rapid evolution of codecs, real-time applications demand more than ever from the complexity of intra-mode selection. Here we show how by employing a refined approach to the rate distortion optimization (RDO) module, we achieve a 5.8% reduction in HEVC complexity and a minor yet notable −0.02% improvement in Bjontegaard Delta Bit Rate (BD-BR). Our method stands out by not only reducing computational load but also by improving bit-rate, a rare feat in the literature. By integrating this approach, future versions of HEVC could witness a significant leap in performance. We believe our findings contribute to the broader context of video compression technologies, inviting further exploration and development. Code is available at https://github.com/drjunaidtariq/ImprovedHEVC/.