In a recent paper, Harary and Kabell discuss the problem of determining the line index of balance of a signed graph. They suggest a solution algorithm which would involve considering all spanning trees of a givengraph in order to comput the index of this graph. The number of spanning tress may grow exponentially with the size of the graph. We show that the problem is indeed difficult, being NP-complete in the general case. Subsecuqnetly, we give an efficient (linear time) algorithm solving the problem for outerplanar graphs with bounded size of interior faces