In this article the authors propose a decentralized control algorithm for a swarm consisted of quadcopters, which are unmanned aerial vehicles (UAV) lifted and propelled by four rotors. The first step was derivation of a quadcopter flight dynamic (math) model and its further linearization. The math model was derived on the basis of Newton and Euler equation of motion. The next step was to design a trajectory control algorithm by using PD regulator for the trajectory error minimization. After designing and approbation of the control algorithm of a unit quadcopter, the authors proceeded further with the task of a group control. Originally, the authors set several requirements to the control algorithm of the quadcopter for a group flight, e.g. cohesion and safety of the flights, decentralization and scalability of the control algorithm. As a ground algorithm they selected C. Reynolds rules designed for "boids". In order to make it possible to switch a quadcopter group flight from the swarm mode to the formation mode, in addition to Reynolds rules the authors developed the forth rule called "Formation". Before designing of the decentralized control for a quadcopter swarm, the authors solved similar tasks related to the kinematic control and dynamic control of the agents moving in 2D. The authors set several experiments in a "Universal Mechanism" and "Matlab" of the quadcopter group flight of10 agents with independent control systems. The above-mentioned experiments proved the efficiency of the designed decentralized control algorithm. The modeling details and experiment results are also presented in the paper.