A two-step chemical etching procedure has been developed for fabricating probes used by scanning near-field optical microscopy. These probes have two tapered regions which can be reproducibly constructed with a wide range of cone angles. The shape of the probe allows it to be used over sample surfaces with deep and narrow regions. Furthermore, our method can be applied to silica glass fibers which are commercially available. To demonstrate, we used these tips to acquire the near-field optical image of a thin layer of polystyrene spheres. Intensity interference patterns were observed. The demonstrated in-plane resolution was estimated to be about 250 nm. This is mainly limited by the diameter of the metal-coated tip. The transmission efficiency of the tip is better than 10-4.