A new observable consequence of the property of invariant item ordering is presented, which holds under Mokken's double monotonicity model for dichotomous data. The observable consequence is an invariant ordering of the item-total regressions. Kendall's measure of concordance "W" and a weighted version of this measure are proposed as measures for this property. Karabatsos and Sheu proposed a Bayesian procedure ("Appl. Psychol. Meas." 28:110-125, 2004), which can be used to determine whether the property of an invariant ordering of the item-total regressions should be rejected for a set of items. An example is presented to illustrate the application of the procedures to empirical data.