For better modeling plane-stress anisotropic plasticity of steel sheets, a direct calibration method is proposed and detailed for establishing a positive and convex sixth-order homogeneous polynomial yield function with up to sixteen independent material constants. The calibration method incorporates parameter identification, convexity testing, and if needed, an adjustment of an initially calibrated but non-convex yield function toward a convex one. Some advantages of the calibration method include (i) a systematic solution of only linear equations for the sixteen material constants of a steel sheet with various degrees of planar anisotropy, (ii) a practical numerical implementation of the necessary and sufficient conditions for convexity certification of the calibrated or adjusted yield function, and (iii) an incremental procedure using a parameterized version of the initially calibrated and non-convex yield function that can always lead to an approximate sixth-order yield function with guaranteed convexity. Results of applying the proposed calibration method to successfully obtain convex sixth-order yield functions are presented for three steel sheets with experimental measurement inputs from various types and numbers per type of uniaxial and biaxial tension tests.