Abstract
The "nonclassical" complex Lorentz transformation, recently introduced as a mathematical convenience by Reulos, is related to the unique factoring of any 4\ifmmode\times\else\texttimes\fi{}4 orthogonal transformation. This factoring also shows, in 4\ifmmode\times\else\texttimes\fi{}4 form, the well known possibility of introducing a 2\ifmmode\times\else\texttimes\fi{}2 complex spin space, in which unimodular transformations are isomorphic to the proper future-preserving Lorentz group.
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