Due to different replication mechanisms between the leading and lagging strands, nucleotide composition asymmetries widely exist in bacterial genomes. A general consideration reveals that the leading strand is enriched in Guanine (G) and Thymine (T), and the lagging strand shows richness in Adenine (A) and Cytosine (C). However, some bacteria like Bacillus subtilis have been discovered composing more A than T in the leading strand. To investigate the difference, we analyze the nucleotide asymmetry from the aspect of AT and GC bias correlations. In this study, we propose a windowless method, the Z-curve Correlation Coefficient (ZCC) index, based on the Z-curve method, and analyzed more than 2000 bacterial genomes. We find that the majority of bacteria reveal negative correlations between AT and GC biases, while most genomes in Firmicutes and Tenericutes have positive ZCC indexes. The presence of PolC, purine asymmetry and stronger genes preference in the leading strand are not confined to Firmicutes, but also likely to happen in other phyla dominated by positive ZCC indexes. This method also provides a new insight into other relevant features like aerobism, and can be applied to analyze the correlation between RY (Purine and Pyrimidine) and MK (Amino and Keto) bias and so on.