The centrifugal instability of stratified two-phase flow in a curved channel is investigated in this work. The fluids are laterally stratified between cylindrical walls of infinite extent. We focus on the limiting case of small capillary numbers (relatively high surface tension), wherein interfacial deformation and associated instabilities are suppressed. The centrifugal instability, caused by unstable gradients of angular momentum, destabilizes the axisymmetric azimuthal base flow. As in single phase Dean flow, an array of vortices is formed within each fluid at the critical Reynolds number. A numerical linear stability analysis is carried out using a recombined Chebyshev Galerkin spectral method, as well as a shooting method. Across the space of physical parameters (volume fractions, density, and viscosity ratios), six critical modes corresponding to distinct secondary flows are observed. These are classified into axisymmetric stationary vortices and rotating spiral vortices (travelling waves). Each category consists of three subtypes based on the relative vortex strength in the fluids: stronger in the outer fluid, stronger in the inner fluid, and comparable strength in both fluids. The critical mode switches amongst these six types as parameters are varied. The outer fluid is found to be more unstable than the inner fluid, even if the fluids have equal physical properties. This is explained using Rayleigh's criterion for inviscid flows. Consequently, the arrangement of fluids has a significant impact on stability. Instability and vortex motion are promoted if the fluid with a higher density, a lower viscosity, and a larger volume fraction is placed on the outer side of the channel. © 2015 AIP Publishing LLC.