Due to the capacity of pan-tilt-zoom (PTZ) cameras to simultaneously cover a panoramic area and maintain high resolution imagery, researches in automated surveillance systems with multiple PTZ cameras have become increasingly important. Most existing algorithms require the prior knowledge of intrinsic parameters of the PTZ camera to infer the relative positioning and orientation among multiple PTZ cameras. To overcome this limitation, we propose a novel mapping algorithm that derives the relative positioning and orientation between two PTZ cameras based on a unified polynomial model. This reduces the dependence on the knowledge of intrinsic parameters of PTZ camera and relative positions. Experimental results demonstrate that our proposed algorithm presents substantially reduced computational complexity and improved flexibility at the cost of slightly decreased pixel accuracy, as compared with the work of Chen and Wang. This slightly decreased pixel accuracy can be compensated by consistent labeling approaches without added cost for the application of automated surveillance systems along with changing configurations and a larger number of PTZ cameras.