  We study the twisted reality condition of Math. Phys. Anal. Geom. 19
(2016),no. 3, Art. 16, for spectral triples, in particular with respect to the
product and the commutant. Motivated by this we present the procedure, which
allows one to "untwist" the twisted spectral triples studied in Lett. Math.
Phys. 106 (2016), 1499-1530. We also relate this construction to conformally
rescaled real twisted spectral triples, and discuss the untwisting of the
`minimal twist' procedure of an even spectral triple.
