Compressed beamforming algorithm is used in the current Wi-Fi standard to reduce the beamforming feedback overhead (BFO). However, with each new amendment of the standard the number of supported antennas in Wi-Fi devices increases, leading to increased BFO and hampering the throughput despite using compressed beamforming. In this paper, a novel index-based method is presented to reduce the BFO in Wi-Fi links. In particular, a k-means clustering-based approach is presented to generate candidate beamforming feedback matrices, thereby reducing the BFO to only the index of the said candidate matrices. With extensive simulation results, we compare the newly proposed method with the IEEE 802.11be baseline and our previously published index-based method. We show approximately 54% gain in throughput at high signal-to-noise (SNR) against the IEEE 802.11be baseline. Our comparison also shows approximately 4 dB gain compared to our previously published method at the packet-error-rate (PER) of 0.01 using MCS index 11. Additionally, we also discuss the impact of the distance metric chosen for clustering as well as candidate selection on the link performance.