We propose a runs test for the hypothesis of symmetry around an unknown median with alternative “stochastically larger than”based on a trimmed runs test for the hypothesis of symmetry around an unknown median with two-tailed alternative proposed in Babativa & Corzo (2010). By a simulation study we show that for samples coming from the Lognormal Distribution, the proposed test maintains the prefixed size and that its empirical power is larger than of the other compared tests proposed in Cabilio & Masaro (1996), Mira (1999) and Miao et al. (2006).