This paper presents a new divide-and-conquer algorithm for the eigenvalue problem of symmetric tridiagonal matrices. The new algorithm oases on bisection and secant iteration, which is different from Cuppen's method and Laguerre iteration. The results of theoretical analysis and numerical testing show that the convergent rate of our algorithm is obviously faster than that of Laguerre iteration presented in [1]. When the problem scale is quite large, with the same requirement of accuracy, more than 40% of the computing time can be reduced by using this new algorithm.