The type IIB matrix model is a promising nonperturbative formulation of superstring theory, which may elucidate the emergence of (3+1)-dimensional space-time. However, the partition function is divergent due to the Lorentz symmetry, which is represented by a noncompact group. This divergence has been regularized conventionally by introducing some infrared cutoff, which breaks the Lorentz symmetry. Here we point out, in a simple model, that Lorentz-invariant observables become classical as one removes the infrared cutoff and that this "classicalization" is actually an artifact of the Lorentz symmetry breaking cutoff. In order to overcome this problem, we propose a natural way to "gauge-fix" the Lorentz symmetry in a fully nonperturbative manner. Thus, we arrive at a new definition of the type IIB matrix model, which also enables us to perform numerical simulations in such a way that the time evolution can be extracted from the generated configurations.