Firstly,the prediction formula of tunnel transversal error considering the correlation of azimuth angles of the two initial sides of the control network outside the tunnel is established.By using the principle of maximum and minimum value of quadratic function,it is deduced that the calculation result of this formula is 0 to 1.732 times of the calculation result of the absolute error prediction formula.If the initial azimuth angle is positively correlated,the transverse error of tunnel penetration will be enlarged,while the negative correlation will decrease or even cancel each other completely.Secondly,the error prediction formula can be used to calculate the minimum value of the transverse median error.Finally,an example is given to show that the prediction error and the optimum through-through position can be more scientifically and accurately determined by selecting the initial azimuth of the combination after the control network is established.