A new approach to solving matrix problems in x-ray fluorescence analysis of trace elements has been applied to the determination of bromine in saline waters and zinc in silicates. The method requires no prior knowledge of the chemical composition of the sample. Marked matrix effects are minimized by dilution, and the problem of variable backgrounds due to residual matrix effects is solved by using a slope-ratio technique. In this proposed technique, the slope of a standard curve prepared from pure solutions is compared with that of spiked samples. The ratio of the slopes of these two curves permits the calculation of an adjusted background which does not significantly differ from that of an absorbent impregnated with the sample matrix free of the element sought. Experimental parameters concerning the technique are presented. The excellent agreement of the zinc and bromine data with analytical results obtained by more conventional methods suggests that the technique can be used for the determination of other trace constituents in geologic materials. Application of the slope-ratio technique to other modes of instrumental analysis appears feasible.