  Penrose's two-spinor notation for $4$-dimensional Lorentzian manifolds can be
extended to two-component notation for quaternionic manifolds, which is a very
useful tool for calculation. We construct a family of quaternionic complexes
over unimodular quaternionic manifolds by elementary calculation. On complex
quaternionic manifolds, which are essentially the complexification of real
analytic quaternionic K\"ahler manifolds, the existence of these complexes was
established by Baston by using twistor transformations and spectral sequences.
Unimodular quaternionic manifolds constitute a nice and large class of
quaternionic manifolds: the conformal change of a unimodular quaternionic
structure is still unimodular quaternionic and the complexes over such
manifolds are conformally invariant. This class of manifolds, including
quaternionic K\"ahler manifolds, are the real version of torsion-free QCFs
introduced by Bailey and Eastwood. We show the ellipticity of these complexes
and its Hodge-type decomposition. We also obtain a Weitzenb\"ock formula to
establish vanishing of the cohomology groups of these complexes for
quaternionic K\"ahler manifolds with negative scalar curvatures.
