We construct an experimental setup, consisting of conical refraction transformation in two biaxial cascade crystals and 4f-system, to realize Unitary transformation of light beam and the manipulation of Poincaré beams on the different parts of Poincaré sphere. The spatial structure of the polarization can be controlled by changing the polarization of the incident beam or rotating the angle between these two crystals. The beams with different SoPs covering the full-Poincaré sphere, part-Poincaré sphere and one point on the sphere are generated for the different angles between crystals. The Unitary transformation of light beam is proposed in the experiment with the invariant intensity distribution. Subsequently, the spin angular momentum is derived from the distribution of polarization measured in our experiment. Moreover, the conversion between orbital angular momentum and spin angular momentum of light beam is obtained by changing the angle between crystals. And the conversion progress can also be influenced by the polarization of incident beam. We realized the continuous control of the spatial structure of the angular momentum density, which has potential in the manipulation of optical trapping systems and polarization-multiplexed free-space optical communication. Up to now, as an intrinsic and fundamental vectorial nature of light, the SoP has attracted wide attention owing to its important role in propagation behaviors, focusing properties, and light-matter interactions. In 2010, Beckely introduced and demonstrated one kind of novel vector beams, named full Poincaré (FP) beams, in the experiment 1,2. One dominant characteristic of FP beams is that the states of polarization (SoPs) in the crosssection cover the entire surface of Poincaré sphere. As a result, any SoP on Poincaré sphere can be found in the FP beams Due to the special SoP distribution, The FP beams have potential for many practical applications in beam shaping 34 , manipulation of particles 5 , generating transverse spin angular momentum 6-8 and significantly reducing turbulence-induced scintillation 9,10. High-order FP beams have been proposed to have benefit in achieving a smooth flat-top transverse profile with steep edge roll-off 11,12. The orders herein are determined by the number of times that the SoP covers all possible polarization states over a Poincaré sphere. Accordingly, there are numerous methods and devices proposed in previous researches for generating the FP beams to achieve further applications, including spatial light modulators 13-15 , uniaxial crystals 16,17 , q-plates and dielectric metasurface 18-20 , geometric phase control inside a laser cavity 21 , and so forth. Conical refraction was demonstrated to be a method to manipulate the SoP of beams as an intrinsic property of biaxial crystals. The cascade conical diffraction phenomenon was comprehensively studied in detail elsewhere 22-25. The further manipulation of SoP were realized, with the multiple-concentric-rings intensity distribution. Based on the characters of the con...