Covariant formulation of f(Q) theory

In Symmetric Teleparallel General Relativity, gravity is attributed to the non-metricity. The so-called "coincident gauge" usually taken in this theory so that affine connection vanishes and metric only fundamental variable. This gauge choice was kept many studies on extensions of such as f(Q) theory. paper, we point out sometimes will make inconsistent. To circumvent problem, reformulate a covariant way with which can find suitable non-vanishing for given metric. We also apply method two important cases: spherically symmetric spacetime homogeneous isotropic expanding universe.