Genetic correlation is a key parameter in the joint genetic model of complex traits, but it is usually estimated on a global genomic scale. Understanding local genetic correlations provides more detailed insight into the shared genetic architecture of complex traits. However, a state-of-the-art tool for local genetic correlation analysis, LAVA, is prone to false inference. Here we extend the high-definition likelihood (HDL) method to a local version, HDL-L, which performs genetic correlation analysis in small, approximately independent linkage disequilibrium blocks. HDL-L allows a more granular estimation of genetic variances and covariances. Simulations show that HDL-L offers more consistent heritability estimates and more efficient genetic correlation estimates compared with LAVA. HDL-L demonstrated robust performance across a wide range of simulations conducted under varying parameter settings. In the analysis of 30 phenotypes from the UK Biobank, HDL-L identified 109 significant local genetic correlations and showed a notable computational advantage. HDL-L proves to be a powerful tool for uncovering the detailed genetic landscape that underlies complex human traits, offering both accuracy and computational efficiency.