The Luminous Face — Carolyn Wells

A group of men discuss the reasons for murder and one announces that he would kill one particular man because he disliked him." Then when the man turns up dead, the others are horrified that he has said something that has put the noose around his own neck, particularly when he offers no alibi. As the police investigate they discover other possible reasons for the murder but in each and all, they find that the alibis hold.