* Think tank FGV says index falls for fifth straight month * Number reflects fragile economy By Silvio Cascione SAO PAULO, Feb 26 (Reuters) - Consumer confidence in Brazil fell in February for the fifth month in a row to the lowest since January 2012, a private survey showed on Tuesday in the latest sign of a fragile recovery in Latin America's largest economy. Brazilian think tank Fundação Getúlio Vargas (FGV) said its consumer confidence index fell to a reading of 116.2 in February from 117.9 in the previous month, down 10 percent from an all-time high in April. Household consumption, supported by low unemployment and rising salaries, has been Brazil's main growth engine over the past decade. It has also fueled inflation, as demand for many services and goods increased at a faster pace than supply. The survey's barometer of the current economic situation dropped to a reading of 128.9, from 131.9 in January, the lowest since April 2010, while the gauge of future expectations slipped to a reading of 109.6 from 110.5, the lowest in one year. Despite the drop, the index remained above its historical average, FGV said in a report. Consumer confidence could recover later this year as the economy picks up steam following several stimulus measures by President Dilma Rousseff's government, economists at Bradesco said in a research note. "The index has been falling since the middle of last year because of the economic slowdown. But it can rise again this year as the economy recovers, given that the labor market remains tight," wrote the economists. The jobless rate fell to a record low of 4.6 percent in December. It rose in January as businesses laid off temporary workers following the holiday season, but was still the lowest on record for the month. FGV's consumer confidence survey is based on interviews conducted with around 2,000 people in seven large Brazilian cities between Jan. 31 and Feb. 23.