The paper reveals a novel linear fractional programming (LFP) tactic for implementing an allpass digital phase-system. The tactic first reduces the system design to an LFP problem, and then further reduces the LFP to a regularized minimization problem for resolving the infeasibility issue. The regularized minimization becomes a linear programming (LP) problem and its objective function to be minimized contains a regularization parameter. To attain the optimum solution, we seek the optimum of the regularization parameter through adopting the bisection-search scheme. After finding the optimum parameter value, we solve the regularized LFP problem and thus yield the optimum design solution, which completes the phase-system design. This paper first details how to reduce the phase-system design to a regularized LFP, and then uses a phase-system design example to demonstrate the superiority of the regularized LFP strategy over various existing design tactics.