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The theory of the so-called Rayleigh–Plateau instability of fluid jets has been widely studied and can be used to predict the breakup length of liquid jets. Recently, in the work of Rosello et al. [J. Fluids Eng. 140(3), 031202 (2018)], the linear theory was enhanced to accurately predict the breakup length of continuous ink jets of Newtonian fluids by accounting for the influence of the nozzle geometry. In the present work, the influence of a shear-thinning behavior is addressed for both the breakup morphologies and breakup lengths in a linear regime. A comparison with the experimental data shows an excellent agreement extending the model of Rosello et al. to a non-Newtonian shear-thinning fluid.