Global stability of distributions of higher corank of derivedlength one

We consider tangent distributions of corank greater than one, each of whose first derived distributions, coincides with the tangent bundle of the underlying manifold. We study a global stability of such distributions. We prove that a one-parameter family of such distributions is described by using a global isotopy of the underlying manifold if the family has a constant integrable subdistribution of corank one. Furthermore, by giving an essential meaning of the subdistribution above from another perspective, we obtain a relation between the result mentioned above and the Gray theorem.