I have to tessellate some surface in OpenGL with rectangular textures. Let it be a single triangle for simplicity. The textures touch each other by sides, and do not overlap. That is done by setting GL_TEXTURE_WRAP_S and GL_TEXTURE_WRAP_T to GL_CLAMP_TO_BORDER and adjusting texture coords properly. Everything goes fine while GL_TEXTURE_MIN_FILTER and GL_TEXTURE_MAG_FILTER is set to GL_NEAREST, but when I want to apply GL_LINEAR filering and/or anisotropic filtering following arifact apperas: textures border pixel's alpha gradually fall to transparent, so that line of background color is visible between neighbouring textures.

How can I avoid this artifact without merging multiple textures to one while linear filtering is preserved?