An apparatus for extracorporeal blood treatment, in particular for hemodialysis, comprising: - a dialyser to which fresh dialysate can be supplied via a supply line of the dialysate, and from which used dialysate can be discharged via a discharge line of the dialysate; - a bypass line which connects the supply line and the discharge line of the dialysate, thereby bypassing the dialyser, and which can selectively be opened for short circuiting the dialyser; - a first measuring device for measuring a variable correlated with the plasma sodium concentration of the blood to be cleaned in the dialyser, the first measuring device being provided directly downstream of the dialyser; - a proportioning unit for automatically adjusting the composition of the dialysate in response to the variable measured such that the plasma sodium concentration of the blood at least at the end of the blood treatment has the same value as at the beginning, and - a control unit for issuing commands and for detecting at least the measured values or conditions of the measuring device, of the proportioning unit, and of first to third valves (7, 9, 10), - a toxin measuring device for measuring a toxin contamination of the used dialysate output by the dialyser, wherein the measured toxin contamination is usable for correcting a conductivity measurement of the first measuring device, wherein - line sections of the supply line and the discharge line of the dialysate located between the bypass line and the dialyser are pumpless, and the control unit is adapted such that, at least at a beginning of the extracorporeal blood treatment, dialysate remains in the dialyser via an interposed bypass operation during standstill, such that after the bypass mode is terminated, the measuring device is adapted to determine the correlated variable. - a dialyser to which fresh dialysate can be supplied via a supply line of the dialysate, and from which used dialysate can be discharged via a discharge line of the dialysate; - a bypass line which connects the supply line and the discharge line of the dialysate, thereby bypassing the dialyser, and which can selectively be opened for short circuiting the dialyser; - a first measuring device for measuring a variable correlated with the plasma sodium concentration of the blood to be cleaned in the dialyser, the first measuring device being provided directly downstream of the dialyser; - a proportioning unit for automatically adjusting the composition of the dialysate in response to the variable measured such that the plasma sodium concentration of the blood at least at the end of the blood treatment has the same value as at the beginning, and - a control unit for issuing commands and for detecting at least the measured values or conditions of the measuring device, of the proportioning unit, and of first to third valves (7, 9, 10), - a toxin measuring device for measuring a toxin contamination of the used dialysate output by the dialyser, wherein the measured toxin contamination is usable for correcting a conductivity measurement of the first measuring device, wherein - line sections of the supply line and the discharge line of the dialysate located between the bypass line and the dialyser are pumpless, and the control unit is adapted such that, at least at a beginning of the extracorporeal blood treatment, dialysate remains in the dialyser via an interposed bypass operation during standstill, such that after the bypass mode is terminated, the measuring device is adapted to determine the correlated variable.