**On a theorem of Radon - Hurwitz**

The classical Hurwitz - Radon theorem states
on the unit sphere S^{n} of (n+1)-dimensional Euclidean space (in case
of odd n) there exists at least r(n) tangent
orthonormal vector fields, where r(n) is the Hurwitz -
Radon number. In the paper a new proof of the Hurwitz - Radon theorem is given.
The proof is based on the construction of the above mentioned vector fields.