A careful and accurate semiempirical calculation of transition matrix elements yielded the oscillator strengths of resonance lines for the lowest np configurations in Mg II. Through an extension of previous work, particular attention was given to the determination of branching ratios for the fine-structure levels in the upper states. The new f-values provide strong theoretical support to the recent astronomical determinations by Fitzpatrick (1997) and could settle the question of the Mg abundance in the interstellar medium. The branching ratio f(3s-4p3/2)/f(3s-4p1/2) = 1.78, a value that deviates from the assumed ratio of 2 used in earlier work.