ThispaperreportsanewderivativeintheEuleriandescriptioninflatspace-thegeneralizedcovariantderivativewithrespecttotime.Thefollowingcontentsareincluded:(a)therestrictedcovariantderivativewithrespecttotimeforEuleriancomponentisdefined;(b)thepostulateofthecovariantforminvariabilityintimefieldissetup;(c)thegeneralizedcovariantderivativewithrespecttotimeforgeneralizedEuleriancomponentisdefined;(d)thealgebraicstructureofthegeneralizedcovariantderivativewithrespecttotimeismadeclear;(e)thecovariantdifferentialtransformationgroupintimefiledisderived.TheseprogressesrevealthecovariantforminvariabilityofEulerianspaceandtime.