  We provide a construction of a class of local and de Sitter covariant
tachyonic quantum fields which exist for discrete negative values of the
squared mass parameter and which have no Minkowskian counterpart. These quantum
fields satisfy an anomalous non-homogeneous Klein-Gordon equation. The anomaly
is a covariant field which can be used to select the physical subspace (of
finite codimension) where the homogeneous tachyonic field equation holds in the
usual form. We show that the model is local and de Sitter invariant on the
physical space. Our construction also sheds new light on the massless minimally
coupled field, which is a special instance of it.
