  The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is
introduced and its characterizations are obtained. We have shown that an
operator on the space $H^2$ is slant H-Toeplitz if and only if its matrix is a
slant H-Toeplitz matrix. In addition the conditions under which slant Toeplitz
and slant Hankel operators become slant H-Toeplitz operators are also obtained.
