The grinding unit according to the invention grinds at least one knife by means of a grinding head (21) comprising a shaft (2). A grinding head holder (3.1, 3.2, 33.1, 5 33.2) holds the grinding head (21). A grinding head rotating drive (7.2) rotates the shaft (2). A shaft guiding assembly (4.1, 4.2, 5.1, 5.2) guides the rotated shaft (2) with respect to the grinding head holder (3.1, 3.2, 33.1, 33.2) along a given trajectory. A grinding head moving drive (7.1) moves the shaft (2) of the grinding head (21) with respect to the grinding head holder (3.1, 3.2, 33.1, 33.2).