In modern real-world applications, it is not uncommon to have larger number of measured variables than the sample size for high-dimensional datasets. In this case, Conventional regression methods fails in this dataset, and sparse regression is needed. Sparse regression is also important in many other cases. The mostly used regularization path for sparse regression is minimizing an l1-regularization term. However this method and its variants have many disadvantages such as bias and introducing more irrelevant features. We introduce inverse scale space (ISS)-a new regularization path for sparse regression, which is unbiased and has better performance in selecting the relevant features. We show why ISS is better than l1-minimization theoretically, and the comparison of both methods is done on synthetic and real data. In addition,we developed an algorithm to accelerate ISS.