Chargaff's rule of intra-strand parity (ISP) between complementary mono/oligonucleotides in chromosomes is well established in the scientific literature. Although a large numbers of papers have been published citing works and discussions on ISP in the genomic era, scientists are yet to find all the factors responsible for such a universal phenomenon in the chromosomes. In the present work, we have tried to address the issue from a new perspective, which is a parallel feature to ISP. The compositional abundance values of mono/oligonucleotides were determined in all non-overlapping sub-chromosomal regions of specific size. Also the frequency distributions of the mono/oligonucleotides among the regions were compared using the Kolmogorov-Smirnov test. Interestingly, the frequency distributions between the complementary mono/oligonucleotides revealed statistical similarity, which we named as intra-strand frequency distribution parity (ISFDP). ISFDP was observed as a general feature in chromosomes of bacteria, archaea and eukaryotes. Violation of ISFDP was also observed in several chromosomes. Chromosomes of different strains belonging a species in bacteria/archaea (Haemophilus influenza, Xylella fastidiosa etc.) and chromosomes of a eukaryote are found to be different among each other with respect to ISFDP violation. ISFDP correlates weakly with ISP in chromosomes suggesting that the latter one is not entirely responsible for the former. Asymmetry of replication topography and composition of forward-encoded sequences between the strands in chromosomes are found to be insufficient to explain the ISFDP feature in all chromosomes. This suggests that multiple factors in chromosomes are responsible for establishing ISFDP.