Abstract
It was proved that local Fourier bases are unconditional bases for modulation spaces M-p.q(w). We prove that the local Fourier bases are unconditional bases for ultramodulation spaces M-p(w gamma) = M-p.p(w gamma), where 0 < p < infinity and w(gamma) = e(s vertical bar x vertical bar gamma), s > 0, gamma is an element of (0, 1), x is an element of R.