The usual transformations (UT) of the 3-vectors E and B that were found by Lorentz and by Poincaré and independently by Einstein in 1905 are generally considered to be the Lorentz transformations (LT) (boosts) of E and B. According to the UT, E in one frame is 'seen' as E' and B' in a relatively moving frame. In Minkowski's last paper, in section 11.6 of Minkowski (1908 Nachr. Ges. Wiss. G?ttingen 53), he defined the vectors (4-vectors in the usual notation) of the electric φ and magnetic ψ fields and discovered that, for example, φ correctly transforms to φ' by the LT. His correct LT are reinvented and generalized in Ivezic (2005 Found. Phys. Lett. 18 301). In this study, we show the essential similarity and some differences between Minkowski's relations in section 11.6 (1908) and the results obtained in Ivezi? (2005). The general expressions for the LT (boosts) and UT of vectors E and B are presented. They are not contained either in Minkowski (1908) or in Ivezi? (2005). The low-velocity limit of the UT and LT is briefly examined.
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