In the process of blood pressure measurement, the pressure of the cuff wrapped around human arms is slowly decreasing for blood pressure analysis. Therefore, a relief valve which renders constant pressure relief rate would improve precision of measurement. Here we demonstrate a novel pressure relief valve for blood pressure monitor. Based on the Bernoulli equation and ideal gas assumption, the relationship of the pressure relief rate and the pressure value is quadratic, leading to a reduction in variation of pressure relief rate. In contrast to the other valve designs, the functionality of this valve is passive and free from any moving parts. Besides, the fabrication of the devices incorporates MEMS technique for bulk fabrication, so the manufacturing cost can be substantially reduced. Thus the device was considered reliable and promising to be commercialized. Two experiments were conducted to test the performance of the valve. First, the relationship between the pressure of cuff and its corresponding flow rate was determined. The results confirmed that their relationship was essentially quadratic. In another experiment, the pressure relief rate was obtained directly. The results demonstrated the relief rate lay between 2 to 4 mmHg/s, satisfying the suggested, relief rate. Hence, the improvement of blood pressure measurement may be achieved for blood pressure monitors.