Abstract. We characterize solutions f, g : R → R of the functional equation f (x + g(x)y) = f (x)f (y) under the assumption that f is locally bounded above at each point x ∈ R. Our result refers to Go lab and Schinzel (Publ Math Debr 6:113-125, 1959) and Wo lodźko (Aequationes Math 2: [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] 1968).Mathematics Subject Classification (2010). Primary 39B22; Secondary 26A03.