1. In a computer system capable of storing and processing data, a method of positioning a plurality of Unicode textual character sequences of like directionality in storage sequence onto a display line comprising the steps of: (a) setting an equal insertion point for all Unicode Bidirectional embedding depth levels at the start point of insertion for the start point of the line; (b) determining if the size of a sequence of like directionality Unicode characters fit within the remaining space available on the line; (c) placing a sequence of like directionality Unicode characters at the insertion point; (d) updating the end point of line insertion according to the dimensions of the sequence of like directionality Unicode characters; (e) generating an insertion stack of insertion minimum and maximum positions for each Unicode Bidirectional embedding depth; and (f) updating entries in the insertion stack for each insertion of a sequence of like directionality Unicode characters.