What is a right way to criticize a published method in my paper? I am writing a research paper, and am fairly new to writing. I am working on a research topic that has not been touched too much. There has only been one other paper published regarding the same topic.

In this other paper, they have a fairly strange methodological approach that almost doesn't make use of the method at hand. My paper is an improvement of their approach; I am wondering what would be the best way to criticize their approach to present my own approach.

As Bob et al. failed to notice, we can actually do this...
There's no need to harshly criticize the authors of the first paper, however strange it seems, even if their approach is plainly wrong. After all, as you say, it appears that they are the only ones who actively worked on that research topic before you.

So, be constructive and build upon what they've done. For instance, you might write something like:


  Bob et al. [1] developed an algorithm to square the circle. This algorithm can square the circle in 198 steps. Here we present a modification of the original algorithm which can square the circle in just 87 steps. This modification is based on the observation that blah blah...