We present a measurement of the correlated bb production cross section. The data used in this analysis were taken with the upgraded CDF detector (CDF II) at the Fermilab Tevatron collider, and correspond to an integrated luminosity of 742  pb−1. We utilize muon pairs with invariant mass 5≤mμμ≤80  GeV/c2 produced by bb double semileptonic decays. For muons with pT≥3  GeV/c and |η|≤0.7, that are produced by b and b quarks with pT≥2  GeV/c and |y|≤1.3, we measure σb→μ,b¯→μ=1549±133  pb. We compare this result with theoretical predictions and previous measurements. We also report the measurement of σc→μ,c→μ, a by-product of the study of the background to bb production.