  Given a spectral triple of compact type with a real structure in the sense of
[Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of
Connes' original definition to accommodate examples coming from quantum group
theory) and references therein, we prove that there is always a universal
object in the category of compact quantum group acting by orientation
preserving isometries (in the sense of [Bhowmick J., Goswami D., J. Funct.
Anal. 257 (2009), 2530-2572]) and also preserving the real structure of the
spectral triple. This gives a natural definition of quantum isometry group in
the context of real spectral triples without fixing a choice of 'volume form'
as in [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572].
