The formulas of binary Edwards curves which can be halved are transformed from the doubling ones by using the symmetry of the formulas. Two situations are to be handled in the derivation by the parameters of the curves. In the case of d₁≠d₂, it is naturally to get a halving algorithm by using the relation of birational equivalence from the Weierstrass curves, the trace functions and the half-trace functions. In the case of d₁＝d₂, a theorem is given to prove it. It is not easy to get a halving algorithm, although the doubling formulas are simpler in this case. Then the efficiency of the halving algorithm is analyzed. The result shows that the efficiency of the halving algorithm cannot catch up with that of the doubling one. Using the ω-coordinate, the halving algorithm is simplified, and is further used to compute the scalar multiplication.