The particle method is an effective approach for simulating complex physical phenomena, such as free-surface flows, and has been widely applied in various industrial fields, including mechanical and chemical engineering. Recently, the development of high-accuracy particle methods has drawn attention as a solution to conventional accuracy-related issues. Notable examples of such methods include the LSMPS method [1], stabilized LSMPS method [2], SPH(2) [3], and compact MPS method [4]. However, most of these high-accuracy methods have been applied only to single-phase flows, and their extension to two-phase flows remains insufficiently explored. This study aims to develop a novel discretization scheme at the interface to enable high-accuracy two-phase flow analysis using the particle method. A major challenge in two-phase flow simulation is accurately and stably computing spatial derivatives of physical quantities at the interface. Due to differential discontinuities in physical quantities across the interface, applying conventional discretization schemes, e.g., standard LSMPS schemes, often leads to numerical instability. To address this issue, we propose a new spatial discretization scheme that incorporates the interface discontinuities including the jump conditions for pressure and the strain rate tensor. The jump conditions are derived analytically based on the governing equations and the stress balance conditions. These equations are enforced as constraints using the Lagrange multiplier method, ensuring accurate evaluation of spatial derivatives of velocity and pressure at the interface while automatically satisfying the interface boundary conditions. To validate the proposed method, verification studies were conducted for droplet oscillation under the influence of surrounding fluids, droplet elongation driven by external flow, and droplet breakup. In each test case, various parameters were considered, including density ratio, viscosity ratio, capillary number, and Reynolds number. The numerical results showed good agreement with theoretical solutions and reference data from the literature, confirming the validity of the proposed method. Detailed results will be presented in the talk.