Combine the mustard, vinegar, and olives in a bowl. Cover and let stand overnight in the refrigerator.
Next day, allow this mixture to come to room temperature. Place butter in the top of a double boiler and allow it to melt. In a bowl, mix egg, sugar, and salt, beating well with a wire whisk. Add this mixture gradually to the warm butter and beat constantly. Gradually add the mustard and vinegar mixture and stir constantly.
When the mixture actually coats a mixing spoon, remove from heat and allow to cool. About 20 minutes before serving, whip in the mayonnaise.
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