This study follows an analogous treatment of data for (HCNO)-C-13-N-14 (K. Islami, B. P. Winnewisser, J. Preusser, and M. Winnewisser, J. Mel. Spectrosc. 176, xxx-xxx (1996)). The model used for the analysis of the Coriolis resonance (00002)/(00010) was extended by G. Wagner, B. P. Winnewisser, M. Winnewisser, and K. Sarka, J. Mel. Spectrosc. 162, 82-119 (1993). In addition to the interaction between the vibrational levels (v(1)v(2)v(3)v(4)v(5))(k) = (00002)(0e) and (00010)(1e), an interaction between the levels (00002)(e,f) and (00010)(1e,f) was included. However, the correlation between the Coriolis parameters describing the two interactions and their correlation with the l-type doubling parameters do not allow a simultaneous fit of both parameters. If the values of both Coriolis parameters are stepped manually, the standard deviation forms a surface. The minimum of the surface of the standard deviation has the form of a shallow valley which leads to ambiguous Coriolis parameters. The aim of this article is to illuminate and compare the ambiguity of the two Coriolis parameters for the four isotopomers (HCNO)-C-12-N-14, (HCNO)-C-13-N-14, (HCNO)-C-12-N-15, and (HCNO)-C-13-N-15 using contour graphs which represent a projection onto a two-dimensional coordinate system of the surface of the standard deviation as a function of the two Coriolis parameters. (C) 1996 Academic Press, Inc.