A complex dielectric constant for double-strand DNA molecules with a length of not greater than 120 base pairs in an aqueous solution containing 30 mM NaCl was systematically measured as a function of chain length in such a way that experimental uncertainties associated with the molecular-weight distribution of specimens were virtually excluded. In contrast to the past experimental and theoretical studies for much longer DNA molecules, both the molar specific dielectric increment and the relaxation time are proportional to the chain length. These scaling rules cannot be accounted for by any theory so far proposed that gives analytical expressions for those two quantities in the long-chain limit.