In place of a real valued differentiable (C2) function on a closed n-dimensional differentiable manifold M, we may more generally consider a differentiable section s in any line bundle L on M, assumed to have structural group Z2, the group of integers modulo two. Since the usual definitions of a critical point and of a non-degenerate critical point are local in nature, and since composing a differentiable real valued function with the function t →—t does not change its set of critical points or its set of non-degenerate critical point, it is clear that we may speak of critical points and nondegenerate critical points of the section s. Unless the bundle has a fixed trivialization however, the index of a non-degenerate critical point must be thought of as a set of two numbers {k, n—k), corresponding to the two indices arising from the two trivializations possible for L restricted to a small enough neighborhood of the point, i.e. corresponding to the two possible ways of reading the index. With this understanding we extend the usual definitions, and call a differentiable (C2) section s of L a Morse section if each of its critical points is non-degenerate.