In this paper, we present a new hybrid branch predictor called the GoStay2, which can effectively reduce indirect misprediction rates. The GoStay2 has two different mechanisms compared to other 2-stage hybrid predictors that use a Branch Target Buffer (BTB) as the first stage predictor: Firstly, to reduce conflict misses in the first stage, a new effective 2-way cache scheme is used instead of a 4-way set-associative. Secondly, to reduce mispredictions caused by an inefficient predict and update rule, a new selection mechanism and update rule are proposed. We have developed a simulation program by using Shade and Spixtools, provided by SUN Microsystems, on an Ultra SPARC/10 processor. Our results show that the GoStay2 improves indirect misprediction rates of a 64-entry to 4K-entry BTB (with a 512-or 1Kentry PHT) by 14.9% to 21.53% compared to the leaky filter.