One of the main problems in the context of source coding is finding a code with minimum average codelength for a given memoryless source. The average codelength should be small because of saving expensive resources, such as hard disk space and transmission bandwidth. In addition to the average codelength, instantaneous decodability of a code should be considered. This is important in many applications such as video compression, where the encoded data must be decoded with the minimum possible delay. Prefix-free codes, for which no codeword is prefix of any other codeword, are instantaneous. It is well known that the Kraft inequality is a necessary and sufficient condition for the existence of a binary prefix-free code with a given codelength vector. Under the Kraft inequality constraint, the average codelength is lower bounded by the entropy. This is why the redundancy, which is the difference between the average codelength and the entropy, is usually considered as a criterion for evaluating the performance of a code for a source. Since assigning prefix-free codewords to the given codelengths is a straightforward task, the main problem is to find the appropriate codelength vector, which minimizes the redundancy under the condition of the Kraft inequality. For a given source, the optimal prefix-free code can be obtained by the well known Huffman algorithm. But in some practical cases symbol probability vector varies in time and/or are not completely known. Hence the problem will be finding a unique code for a justify; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" Consider the case where the only information about the source is its alphabet size and the order of symbol probabilities. In other words, the justify; TEXT-INDENT: -18pt; MARGIN: 0cm 0cm 0pt 25.1pt; unicode-bidi: embed; DIRECTION: ltr; mso-list: l0 level1 lfo1" · The M code is a fixed code for all monotone sources with N symbols, i.e. it is enough to apply the Huffman algorithm on the average distribution and employ the derived code on all sources in the justify; TEXT-INDENT: -18pt; MARGIN: 0cm 0cm 0pt 25.1pt; unicode-bidi: embed; DIRECTION: ltr; mso-list: l0 level1 lfo1" · The average redundancy of the M code is an upper bound on the average redundancy of the Huffman code. Thus the performance of the M code is Keywords: Redundancy, Average codeword length, Kraft inequality, Huffman code, M code, MinAve criterion, Average distribution, Multiplicity vector.