Symmetries of nanometer-scale local structures in the rhombohedral and orthorhombic phases of potassium niobate (KNbO3) have been examined using convergent-beam electron diffraction. Nanometer-size local structures with rhombohedral symmetry have been discovered in the orthorhombic phase of KNbO3. It has been found that the structure of the orthorhombic phase of KNbO3 is formed as an average of two variants with rhombohedral symmetry. This fact indicates that the phase transformation between the orthorhombic and rhombohedral phases has an order-disorder character. The result is analogous to the case of BaTiO3, which we already reported [Tsuda, Phys. Rev. B 86, 214106 (2012)].