The absence of the paramagnetic contribution in the low-temperature specific heat (C) of Zn-doped cuprates has attracted much attention recently. The phenomenon was usually explained as possible screening in the superconducting state. We have measured C of La1.9Sr0.1Cu0.98Zn0.02O4 which is not superconducting. Intriguingly, The upper limit of the magnetic contribution is found to be two orders of magnitude smaller than the expected value with no screening effect. This result puts the above explanation in a serious jeopardy.