Context :

Aims : We used 12,530 photometrically-selected blue horizontal branch ( BHB ) stars from the Sloan Digital Sky Survey ( SDSS ) to estimate the total extinction of the Milky Way at the high Galactic latitudes , R _ { V } and A _ { V } in each line of sight .

Methods : A Bayesian method was developed to estimate the reddening values in the given lines of sight .
Based on the most likely values of reddening in multiple colors , we were able to derive the values of R _ { V } and A _ { V } .

Results : We selected 94 zero-reddened BHB stars from seven globular clusters as the template .
The reddening in the four SDSS colors for the northern Galactic cap were estimated by comparing the field BHB stars with the template stars .
The accuracy of this estimation is around 0.01 mag for most lines of sight .
We also obtained < R _ { V } > to be around 2.40 \pm 1.05 and A _ { V } map within an uncertainty of 0.1 mag .
The results , including reddening values in the four SDSS colors , A _ { V } , and R _ { V } in each line of sight , are released on line .
In this work , we employ an up-to-date parallel technique on GPU card to overcome time-consuming computations .
We plan to release online the C++ CUDA code used for this analysis .

Conclusions : The extinction map derived from BHB stars is highly consistent with that from Schlegel , Finkbeiner & Davis ( 1998 ) .
The derived R _ { V } is around 2.40 \pm 1.05 .
The contamination probably makes the R _ { V } be larger .