This work deals with a new class of discrete orthogonal transform. This transform is a parametric transform with rotation angles as parameters. We named this transform „RABOT”. The main goal of work is to summarize RABOT calculating algorithms, to calculate quantization errors, and to make a brief review of applications. To accomplish the goal we state the following basic tasks: Perform the review of literature on discrete orthogonal transform; perform the review of literature on the use of angles in signal processing; discover, compare, and summarize RABOT synthesis methods; analyze errors of RABOT transform; propose the ways to minimize errors; summarize the properties of RABOT. Before defining the RABOT and its subclasses, to be sure that this new transform is an original one, we have thoroughly reviewed the literature on discrete orthogonal transform and on the use of angles in signal processing. Synthesis methods of RABOT basic functions, as well as signal analysis and synthesis in RABOT are investigated. Implementation of the transform in real devices, using CORDIC, LININT, and trigonometric function table, is analyzed. A detailed analysis of quantization error is provided for devices with fixed point arithmetic. Error analysis is performed using analytical and numerical methods. Analytical method is based on symbolic calculations. Numerical method is based on error simulation and the result is generalized by fitting the analytical expression. The main results of the work are: classification of transforms, algorithms for synthesis of RABOT basis functions, error estimation for applications in real devices with fixed point arithmetic. This work may be very useful for obtaining a detailed description of RABOT and its subclasses, as well as for calculating quantization error caused by implementation of RABOT in real devices with fixed point arithmetic.