NGC 362 is a non-common Type II Galactic globular cluster, showing a complex pseudo two-colour diagram or 'chromosome map'. The clear separation of its stellar populations in the colour-magnitude diagram and the distribution of the giant stars in the chromosome map strongly suggests that NGC 362 could host stars with both cluster-nominal, as well as enhanced heavy-element abundances, and one of them could be iron. However, despite previous spectroscopic observations of NGC 362, no such iron variation has been detected. Our main goal is to confirm or disprove this result by searching for any internal variation of [Fe/H], which would give us insight into the formation and evolution of this interesting globular cluster. In this paper, we present the abundance analysis for a sample of 11 red giant branch members based on high-resolution and high S/N spectra obtained with the MIKE echelle spectrograph mounted at the Magellan- Clay telescope. HST and GAIA photometry and astrometry has been used to determine atmospheric parameters and membership. We obtained Teff, log(g), and vt for our target stars and measured the mean iron content of the sample and its dispersion with three different methods, which lead to [Fe/H]_1_ = -1.10 +/- 0.02, [Fe/H]_2_ = -1.09 +/- 0.01, and [Fe/H]_3_ = -1.10 +/- 0.01, while the internal dispersion turned out to be {sigma}_[Fe/H]1_ = 0.06 +/- 0.01, {sigma}_[Fe/H]2_ = 0.03 +/- 0.01, and {sigma}_[Fe/H]3_ = 0.05 +/- 0.01, respectively. The error analysis gives an internal dispersion due to observational error of 0.05 dex. Comparing the observed dispersion with the internal errors, we conclude that NGC 362 does not show any trace of an internal iron spread.