Recently, studies have shown evidence of log-periodic behavior in non-hierarchical systems. A known case of log-periodicity or discrete scale invariance are systems that have a geometric hierarchy, for example the model Potts on the diamond structure. The usual solutions of the renormalization group show that such systems have power laws 1/(x)ˆb with complex exponents b ∈ C when near a critical point. An interesting fact is the emergence of such properties in real systems, for instance rupture and breakdown of complex materials and financial crashes. These may be examples of complex systems with self-organized criticality (SOC). The detection of discrete scale invariance, or log-periodicity in non-hierarchical systems presents numerous difficulties. Parametric estimates using log-periodic functions can be flawed due to large fluctuations in values, beyond the problem of degeneracy and multiple local minima in parametric regression estimation. For these reasons most research focuses on the use of nonparametric methods in detecting discrete scale invariance. A method widely used for the study of log-periodic data is to make a change of variable t for a new log-time τ ≡ ln(tc − t), then to study the power spectrum of the new series thus generated. A consequence of this method is the non-uniformity of the sample data, i.e. unequal spacing between data points. The FFT-based techniques are not applicable, but one solution is to use the Lomb periodogram of Scargle, which is suitable for unevenly sampled points. We applying this method to study the Brazilian financial market, with the aim of detecting discrete scale invariance in the Bovespa (Bolsa de Valores de S ̃ao Paulo) stock market index. Some historical price series have been selected for the periods in 1999, 2001 and 2008. We report evidence of detection of possible log-periodicity before breaks.