It is human nature to seek a cause for an event, but sometimes this natural tendency can lead us to making erroneous accusations against innocent individuals. Whether the infraction is large or small, wrongfully accusing someone, such as your brother, can lead to feelings of hurt, frustration, anger and distrust. If you have mistakenly accused your brother of doing something that he hasn't done or isn't responsible for, the best thing that you can do to remedy the situation is to offer a sincere and timely apology.
Elements of An Effective Apology
Make a clear statement of regret and remorse to your brother for having accused him. It is important that you do not simply say you are sorry without also detailing specifically that you are sorry for having accused your brother of something. If you just say that you are sorry without providing the reason why, your apology to your brother may be perceived as flippant or insincere. Conversely, if you only mention that you should not have accused him but fail to specifically state that you are sorry for having done so, your brother may perceive your apology to be half-hearted.
Ask your brother to forgive you. Try to avoid offering overly detailed explanations or excuses for your behavior, as these will undermine your apology and may lead your brother to believe you are not truly sorry. Regardless of why you accused your brother, simply state your remorse and ask that he forgive you. Asking forgiveness acknowledges that you have done something wrong that has hurt your brother and lets him know that it is important to you that you repair the damage and maintain the relationship.
Try to empathize with your brother. It can be very unsettling and frustrating to be accused falsely. Try to consider how he might be feeling. By developing a sense of how your brother is responding to your accusation and how he has been made to feel, you can offer a more sincere and tailored apology. For example, you may want to mention your interpretation of his feelings in your apology by saying "I am sorry for accusing you, I imagine that must have made you feel frustrated and angry."
Make an attempt to reconcile the situation by offering some form of appropriate and related compensation. For example, if you publicly accused your brother or if other people are aware of the accusation, you may want to offer to set the record straight and to let other people know, in addition to your brother, that you were wrong in your accusation and that your brother is in fact innocent. Clearing your brother's name may help to relieve some of the negative feelings he is experiencing and may help him to feel more comfortable forgiving your accusation.