A decoding method for decoding a coded picture included in a coded stream, comprising: obtaining, from a header (D100;D201) of the coded stream, a plurality of quantization parameter sets (D104 to D110;D205) each including a quantization matrix (D106,D110); parsing an identifier (D114;D215) for identifying a quantization parameter set from a header (D112;D213) of the coded picture included in the coded stream; selecting at least one quantization parameter set from among the plurality of quantization parameter sets (D104 to D110;D205), based on the parsed identifier(D114;D215); obtaining a quantization matrix (D106,D110) included in the selected quantization parameter set; parsing an update flag (D116,D120) from the header (D112,D213) of the coded picture; and determining whether the parsed update flag (D116,D120) has a predetermined value; generating a new quantization matrix when the update flag (D116,D120) has the predetermined value; and decoding (S412,S414) the coded picture (i) by inversely quantizing transformed coefficients of the coded picture using the generated new quantization matrix and a quantization parameter when the update flag (D116,D120) has the predetermined value, and (ii) by inversely quantizing transformed coefficients of the coded picture using the obtained quantization matrix (D106,110) included in the selected quantization parameter set when the update flag (D116,D120) does not have the predetermined value; wherein inversely quantizing of a transformed coefficient of the coded picture is performed according to the expression: AbsCoeff i j = abs QuantizedCoeff i j < < 7 − Offset i j * LevelScale * QMatrix i j > > QShift. where QuantizedCoeff[i][j] denotes a quantized transformed coefficient, QMatrix[i][j] denotes a quantization scaling matrix, Offset[i][j] denotes a quantization offset matrix, and LevelScale and QShift denote values controlled by the quantization parameter; characterized in that said generating a new quantization matrix comprises: parsing an update parameter (D118,D122;D221) from the header (D112;D213) of the coded picture; and generating the new quantization matrix by adding or multiplying the update parameter (D118,D122;D221) to or by the values of the obtained quantization matrix; wherein the new quantization matrix is at least one of the quantization scaling matrix and the quantization offset matrix. obtaining, from a header (D100;D201) of the coded stream, a plurality of quantization parameter sets (D104 to D110;D205) each including a quantization matrix (D106,D110); parsing an identifier (D114;D215) for identifying a quantization parameter set from a header (D112;D213) of the coded picture included in the coded stream; selecting at least one quantization parameter set from among the plurality of quantization parameter sets (D104 to D110;D205), based on the parsed identifier(D114;D215); obtaining a quantization matrix (D106,D110) included in the selected quantization parameter set; parsing an update flag (D116,D120) from the header (D112,D213) of the coded picture; and determining whether the parsed update flag (D116,D120) has a predetermined value; generating a new quantization matrix when the update flag (D116,D120) has the predetermined value; and decoding (S412,S414) the coded picture (i) by inversely quantizing transformed coefficients of the coded picture using the generated new quantization matrix and a quantization parameter when the update flag (D116,D120) has the predetermined value, and (ii) by inversely quantizing transformed coefficients of the coded picture using the obtained quantization matrix (D106,110) included in the selected quantization parameter set when the update flag (D116,D120) does not have the predetermined value; wherein parsing an update parameter (D118,D122;D221) from the header (D112;D213) of the coded picture; and generating the new quantization matrix by adding or multiplying the update parameter (D118,D122;D221) to or by the values of the obtained quantization matrix; wherein the new quantization matrix is at least one of the quantization scaling matrix and the quantization offset matrix.