Microelectromechanical system (MEMS) butterfly gyroscope is one of the most potential high-precision $ir=textit{x}$ / $textit{y}$ -axis gyroscopes, whose vibration beam as the critical component has a large effect on its performance. This article researched the influence of the spindle azimuth on the vibration beam by building a mathematical model, which found the larger and more robust spindle azimuth to process variation benefited the sensitivity and quadrature error. A novel butterfly gyroscope with a concave vibration beam was proposed. And the effect of its parameters on spindle azimuth was analyzed theoretically, which helped to propose a method for designing the most optimal concave vibration beam. In the presence of the same fabrication error, the robustness of the spindle azimuth to process variation was improved about double theoretically compared to the former vibration beam. The fabrication process and the corresponding control system were designed and conducted. Experiments appeared that the butterfly gyroscope with a concave vibration beam was nearly half in the quadrature error ratio (avg 0.869) than the former (avg 1.669). More importantly, the distribution of the quadrature error in the novel butterfly gyroscopes was more concentrated. Their standard deviation was calculated as 0.292, which was nearly half of that of the oblique beam (0.579). It meant the concave beam appeared to have better robustness to process variation.