We introduce efficient algorithms for the τ-adic sliding window method, which is a scalar multiplication algorithm on Koblitz curves over F2m. The τ-adic sliding window method is divided into two parts: the precomputation part and the main computation part. Until now, there has been no efficient way to deal with the precomputation part; the required points of the elliptic curves were calculated one by one. We propose two fast algorithms for the precomputation part. One of the proposed methods decreases the cost of the precomputation part by approximately 30%. Since more points are calculated, the total cost of scalar multiplication is decreased by approximately 7.5%.