This paper presents an extended interaction klystron (EIK) operating at 0.22 THz based on a four-sheet-beam orthogonal interconnection structure (OIS). The proposed OIS comprises four vertically positioned trapezoidal line structures, significantly enhancing the coupling efficiency between cavities and achieving optimal interactions with the TM81 mode. This study investigates the dispersion characteristics and field distribution numerically, while the optimal working parameters and output structure were analyzed using the particle-in-cell (PIC) studio. The parameters of each cavity and the selection of five intermediate cavities were finalized by calculating the beam conductance, external quality factor, and stagger-tuning. The EIK generated a continuous 480 W output power with a four-sheet-beam at 17.5 kV and a current density of 200 A/cm2 from an input drive signal of 20 mW. The gain was approximately 43.8 dB.