The invention is classified as a flexible staircase of passenger airplane stairs in the field of workflows and transport. The parallelogram staircase consists of a platform and an optional number of steps, supported by the bottom and top connection, on which the stairs and the platform are articulately fastened to form parallelograms and so that their walking surfaces are permanently parallel. To increase the working area, the distance between the attachments (1a, 1b) of the bottom and the top connection to the undercarriage is smaller than the attachments (2a, 2b) of an individual step or platform to the bottom and top connection is of key importance, thereby changing the slope of the staircase and enabling the change of the incline of all walking surfaces of the passenger stairs. Due to the change of the staircase geometry and the slope of the walking surfaces while changing the height of the platform, the attachments of the bottom connection to the undercarriage are linearly movable, while the bottom connection has the appropriate shape for the position of the attachments. The top connection is mounted to the undercarriage articulately.