We strengthen the non-deterministic time hierarchy theorem of \cite{Cook72, Seiferas-Fischer-Meyer78, Zak83} to show that the lower bound holds against sublinear advice. More formally, we show that for any constants c and d such that 1 c d , there is a language in \NTIME ( n d ) which is not in \NTIME ( n c ) n 1 d . The best known earlier separation \cite{Fortnow-Santhanam-Trevisan04} could only handle o ( log ( n )) bits of advice in the lower bound.