This paper analyzes whether procedures for multiple comparison derived in Hyodo et al.(2013) work for an unbalanced case and under non-normality. We focus onpairwise multiple comparisons and comparisons with a control among mean vectors, and show that the asymptotic properties of these procedures remain valid in an unbalanced high-dimensional setting. We also numerically justify that the derived procedures are robust under non-normality, ie, the coverage probability of these procedures can be controlled with or without the assumption of normality of the data.