Recently, many biological studies reported that two groups of genes tend to show negatively correlated or opposite expression tendency in many biological processes or pathways. The negative correlation between genes may imply an important biological mechanism. In this study, we proposed a FCA-based negative correlation algorithm (NCFCA) that can effectively identify opposite expression tendency between two gene groups in gene expression data. After applying it to expression data of cell cycle-regulated genes in yeast, we found that six minichromosome maintenance family genes showed the opposite changing tendency with eight core histone family genes. Furthermore, we confirmed that the negative correlation expression pattern between these two families may be conserved in the cell cycle. Finally, we discussed the reasons underlying the negative correlation of six minichromosome maintenance (MCM) family genes with eight core histone family genes. Our results revealed that negative correlation is an important and potential mechanism that maintains the balance of biological systems by repressing some genes while inducing others. It can thus provide new understanding of gene expression and regulation, the causes of diseases, etc.