We studied the changes in the higher-order structure of a megabase-size DNA (S120-1 DNA) under different spermidine (SPD) concentrations through single-molecule observations using fluorescence microscopy (FM) and atomic force microscopy (AFM). We examined the difference between the folding transitions in S120-1 DNA and sub-megabase-size DNA, T4 DNA (166 kbp). From FM observations, it is found that S120-1 DNA exhibits intra-chain segregation as the intermediate state of transition, in contrast to the all-or-none nature of the transition on T4 DNA. Large S120-1 DNA exhibits a folding transition at lower concentrations of SPD than T4 DNA. AFM observations showed that DNA segments become aligned in parallel on a two-dimensional surface as the SPD concentration increases and that highly intense parallel alignment is achieved just before the compaction. S120-1 DNA requires one-tenth the SPD concentration as that required by T4 DNA to achieve the same degree of parallel ordering. We theoretically discuss the cause of the parallel ordering near the transition into a fully compact state on a two-dimensional surface, and argue that such parallel ordering disappears in bulk solution.