We introduce a novel blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ), to reliably transmit short binary packets over unknown finite impulse response systems as used, for example, to model underspread wireless multipath channels. In MOCZ, the information is modulated onto the zeros of the transmitted signals $z-$transform. In the absence of additive noise, the zero structure of the signal is perfectly preserved at the receiver, no matter what the channel impulse response (CIR) is. Furthermore, by a proper selection of the zeros, we show that MOCZ is not only invariant to the CIR, but also robust against additive noise. Starting with the maximum-likelihood estimator, we define a low complexity and reliable decoder and compare it to various state-of-the art noncoherent schemes.