There is very little evidence that the narrator has just cause for murder. The narrator, without evidence, believes that the old man with whom he lives wishes him harm. His sole "evidence" is the man's cloudy eye, which he thinks indicates his willingness to harm him, even though all exterior does not support such a claim in any way.
Some evidence for this argument can be supported by the lines which read:
" It is impossible to say how first the idea entered my brain, but, once conceived, it haunted me day and night. Object there was none. Passion there was none. I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire. I think it was his eye! Yes, it was this! One of his eyes resembled that of a vulture—a pale blue eye with a film over it. Whenever it fell upon me my blood ran cold, and so by degrees, very gradually, I made up my mind to take the life of the old man, and thus rid myself of the eye for ever."