We present a new method for high precision measurement of both strontium and barium isotopes. Our method is primarily designed for extraterrestrial samples but is actually suitable for any sample, particularly for sampLes with Low Sr and Ba concentrations and complex matrices. The main separation of Sr, Ba and matrix elements is done with Eichrom (TM) Sr resin, which provides a quick and easy way to separate all three fractions with Lithe further purification needed. ALL isotope data were acquired on a Thermal Ionization Mass Spectrometer (TIMS) Thermo Triton (TM) plus. Isotopic ratios were calculated using a muLtidynamic acquisition scheme when possible. The decay of the amplifiers associated with Faraday cups was carefully tuned to ensure that there was no effect in the muLtidynamic acquisition mode. This technique improves the uncertainty for Sr-84/Sr-86, Sr-86/Sr-86 and Ba-135/Ba-136 by a factor of two compared with previous data obtained in static collection mode. The uncertainties attainable with our new method were 2 ppm and 19 ppm (2 s.d.) for the Sr-86/Sr-86 and Sr-84/Sr-86 ratios, respectively and 4 ppm (2 s.d.) for the Ba-135/Ba-136 ratio. The low-abundance Ba-132 isotope was measured with a Faraday cup equipped with a 10(12) Omega resistor to improve the precision of the Ba-132/Ba-136 ratio. We assessed the robustness of our method by measuring several terrestrial rock standards. The use of the muLtidynamic calculation shows the small, but resolvable difference of 20-30 ppm previously observed for the Sr-84/Sr-86 ratio between Earth and isotopic standard SRM NIST 987 (formerly NBS 987), which rules out the hypothesis of a Sr-84 contamination or a fractionation of NIST 987 [Moynier et al., Astrophys. J., 2012, 758, 45; Paton et al., Astrophys. J., 2013, 763, [401 and is in agreement with the results of Hans et al., Earth Planet. Sci. Lett., 2013, 374, 204-214.