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In general, the softer the stiffness of a linear vibration isolator the better the performance of isolation can be achieved. However, the stiffness of the isolator cannot be made too soft because it needs a sufficient stiffness to hold the load. This is the most critical limitation of a linear vibration isolator. Recently, a HSLDS(high-static-low-dynamic-stiffness) magnetic vibration isolator was proposed to overcome this fundamental limitation. The suggested isolator utilizes two pairs of attracting magnets that introduces negative stiffness. Previously, this new type of vibration isolator was merely introduced and showed a possibility of practical use. In this paper, detailed dynamics of the HSLDS magnetic isolator are studied using computer simulations. Then, the isolation performance is examined for various design parameters to aid the practical use.