A bus bar for an electrolyte sheet is provided that includes a bus strip of electrically conductive material in contact with a side edge of the cell or cells in the electrolyte sheet, wherein the amount of material in shoulder portions of the bus strip decreases as the strip approaches end portions of the cell edge to reduce stress. Preferably, such material reduction is accomplished by tapering the shoulder portions of the bus strip. The tapered shape of the shoulders reduces the amount of electrical conductor needed to form the bus bar. The stress reducing bus bar also includes a lead which is orthogonally oriented with respect to the longitudinal axis of the side edge of the cell. The tapered shape of the shoulder portions of the bus strip, in combination with the orthogonally oriented lead, reduces stresses that would otherwise occur between the bus bar and the electrolyte sheet as a result of differences in the thermal coefficient of expansion. The specific shape of the taper in the shoulder portions is selected such that I 2 R losses are substantially minimized along the longitudinal axis of the bus strip.