The aim of the article is to analyze the process of a cabinet coalition formation in a double non-standard situation: a) in the Westminster-model state (New Zealand), in which until 1996 single-party cabinets dominated and coalition bargaining was arranged very rarely; b) in a context of negotiations conducted simultaneously by a pivotal party with a high potential for political blackmail towards two main potential coalition partners. The main research question is about similarities and differences between Westminster and classical processes of government coalition formation, during which the formateur negotiates with another party or parties the coalition agreement. The main research method used in the analysis is a case study. The article was extended to sketch the institutional context and some elements of historical analysis (in those points where the historical background had an impact on the analysed coalition).