We deal with the fully parabolic 1d chemotaxis system with diffusion $1/(1+u)$. We prove that the above mentioned nonlinearity, despite being a natural candidate, is not critical. It means that for such a diffusion any initial condition, independently on the magnitude of mass, generates global-in-time and bounded solution. In order to prove our theorem, we establish a new Lyapunov-like functional associated to the system. This talk is based on a recent joint project with Tomasz Cieslak.