If X is a q-convex complex manifold then dimcH~(X, Y) = q for any coherent analytic sheaf. This is a result of Andreotti and Grauert [1] using abstract functional analysis methods. In Buchner, Fritzsche, Sakai [5] the special situation X=IP,\Y was investigated, where Y is an "extremely" homogeneous algebraic submanifold of IP~ (These Y's were called normally homogeneous in [51). According to Barth [31 X is q-convex for q =codimr Y It was shown in Buchner, Fritzsche, Sakai that for these special domains X the group H'~(X, g2 ~) + 0 for an m > q that could be explicitly given. In this paper the special example of X =IPs\IP 1 • IP a will be considered and an elementary method given to calculate the dimension of H2(X, ~2s). The definition of ~ech cohomology in terms of cocycles and coboundaries is explicitly used as well as the fiber structure of X. The idea is to find a special open covering ![ of X such that Hz(x, Y25)~HZ(lI, f25). Next elements of ZZ(!l, 0 5) (which are convergent power series) are approximated by elements of "finite order", all but finitely many of which are shown to lie in BZ(lI, f25). Then (modulo these finitely many elements) the limit is shown to lie in B2(Lt, 05). The key proposition here is proposition 2. Actually it is shown that dimeHZ(1P~\lPj x IP2, f2s)= 1 and a generator of the cohomology can be explicitly given. It seems likely that this method can be generalized to the case where X is a principal fiber bundle over a compact complex manifold with Stein fibers. Hartshorne and Ogus have informed us that the problem can also be handled by translating it into algebraic geometry using GAGA-methods and using the results of Hartshorne ([8]) and Ogus ([10], especially theorem 2.t.). Their method is completely different from our "elementary" proof. The significance of the result is two-fold: first, that H2(IPs\Y, f2 s) consists only of a de Rham part so that the nonvanishing of this group is related to a topological obstruction which was identified in [5] as the cut locus of Y in lips;