We investigate the robustness of ``noncollective'' rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal $I(I+1)$ behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin-${I}_{\mathrm{max}}$ ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.