Several tools to measure attachment style in adulthood have been developed in the past three decades; however, their dimensionality is still unclear, with the main unanswered question being that of global attachment. In the Relationship Structures Questionnaire, ECR RS (Fraley et al., 2011), respondents rate their relationship to four attachment figures (mother, father, close friend and partner). The paper assesses its dimensionality to test the structure of global attachment. We used a Czech sample (N = 1023) and an international sample (Hudson et al., 2015; N = 1095) to compare a hierarchical model, in which the figure specific attachment factors are partially the product of global attachment, with a bi-factor model, in which the global attachment factors directly affect the responses in questionnaires. The bi-factor model fits the data better and it lends support to the hypothesis that global attachment relates to human behaviour directly and is not mediated by specific attachment to different figures. The limitations of this finding are discussed.