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We have investigated the local structure of BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>-based layered materials by Bi L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>-edge extended X-ray absorption fine structure (EXAFS) measurements performed on single crystal samples with polarization of the X-ray beam parallel to the BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> plane. The results confirm highly instable nature of BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> layer, characterized by ferroelectric like distortions. The distortion amplitude, determined by the separation between the two in-plane (Bi-S1) bonds, is found to be highest in LaO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.77</mn></mrow></msub></semantics></math></inline-formula>F<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.23</mn></mrow></msub></semantics></math></inline-formula>BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>R∼0.26 Å and lowest in NdO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.71</mn></mrow></msub></semantics></math></inline-formula>F<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>0.29</mn></mrow></msub></semantics></math></inline-formula>BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>R∼0.13 Å. Among the systems with intrinsic doping, CeOBiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> shows smaller distortion (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>R∼0.15 Å) than PrOBiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>R∼0.18 Å) while the highest distortion appears for EuFBiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> revealing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>R∼0.22 Å. It appears that the distortion amplitude is controlled by the nature of the RE(O,F) spacer layer in the RE(O,F)BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> structure. The X-ray absorption near edge structure (XANES) spectra, probing the local geometry, shows a spectral weight transfer that evolves systematically with the distortion amplitude in the BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>-layer. The results provide a quantitative measurements of the local distortions in the instable BiS<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>-layer with direct implication on the physical properties of these materials.