This paper considers the existence of local complex foliations of smooth CR submanifolds near a point z, where the dimension of the Levi null space might jump. Suppose z is generic in the sense that the dimension of the Levi null space is at least q in a neighborhood of z and the set where this dimension is exactly q is dense in a neighbourhood of z. The author shows the existence of a Levi foliation at z to be equivalent to the existence of a smooth, constant and maximal rank solution (near z) of the system \(L(z)x(z)=0\), where L(z) is the Levi matrix. In addition to the references listed in the paper under review, the reader interested in this subject should also be aware of two papers by \textit{M. Freeman} in Ann. Math. 106, 319-352 (1977; Zbl 0372.32005), and ibid. 119, 465-510 (1984; Zbl 0572.58001).