In this study the SrBi$_2$Ta$_2$$O_{9}$ (SBT) thin films were etched by using magnetically enhanced inductively coupled Ar/CHF$_3$plasma as function of CHF$_3$/(Ar+CHF$_3$)gas mixing ratio. Maximum etch rate of SBT thin films was 1650 $AA$/min and the selectivities of SBT to Pt and photoresist(PR) were 1.35 and 0.94 respectively under CHF$_3$/(Ar+CHF$_3$) of 0.1 For study on etching mechanism of SBT thin film X-ray photoelectron spectroscopy (XPS) surface analyses and secondary ion mass spectrometry (SIMS) mass analysis of etched SBT surfaces were performed. Among the elements of SBT thin film. M(Sr, Bi, Ta)-O bonds are broken by Ar ion bombardment and form SrF and TaF$_2$by chemical reaction with F. SrF and TaF$_2$are removed more easily by Ar ion bombardment. Scanning electron microscopy(SEM) was used for the profile examination of etched SBT film and the cross-sectional SEM profile of etched SBT film under CHF$_3$(Ar+CHF$_3$) of 0.1 was about 85$^{circ}$X>