This paper presents a method for constructing a singularity-free attitude control system, based on the Euler angles for an unmanned underwater vehicle (UUV), operated at large angles of inclination. This method consists in constructing a hybrid control system with switching between control systems using 3-2-1 (yaw, pitch, roll) and 3-2-3 Euler angle sets. The resulting control system is insensitive to problems of singularity and non-uniqueness of Euler angles, and also maintains high quality at any angles of inclination. Additionally, an experiment was carried out which showed that in some cases the approach based on Euler angles has an advantage over the approach based on quaternions. The performance of the control system at large pitch angles was tested on the nonlinear model of UUV "Aqua-MO" and has a better quality compared to the approach based on quaternions. The increase in the number of tasks requiring the operation of the UVV at large angles of inclination motivated the research agenda. The development of highly maneuverable UUVs, require singularity-free attitude control systems that maintain the required quality at any inclinations of UUVs. However, traditional control systems use Euler angles and are inoperative at pitch angles of ±90°, which prevents their use in new UUVs. The results obtained in the paper can be used in the design of control systems for new highly maneuverable UUVs, and also contribute to the expansion of the working angles of traditional control systems and the use of accumulated experience to solve new problems.