1. An image coding method comprising: obtaining a picture in a video sequence, the picture containing a first signal and a second signal; partitioning the obtained picture, to generate at least one processing block as a processing unit for intra prediction; performing, on each of the at least one processing block, a first intra prediction that selects one intra prediction mode from a first set of candidates based on a component of the first signal contained in the processing block; performing, on each of the at least one processing block, a second intra prediction that selects one intra prediction mode from a second set of candidates based on a component of the second signal contained in the processing block; and performing a first coding process that predictively codes the component of the first signal contained in each of the at least one processing block by using the intra prediction mode selected in the first intra prediction, and performing a second coding process that predictively codes the component of the second signal contained in each of the at least one processing block by using the intra prediction mode selected in the second intra prediction, wherein: the first set of candidates includes a plurality of intra prediction modes, and the second set of candidates includes at least one intra prediction mode, having no dependency between the second intra prediction and the first intra prediction, of the plurality of intra prediction modes, the first intra prediction and the second intra prediction are performed in parallel, the first set of candidates includes 35 intra prediction modes from mode 0 to mode 34 defined in a High Efficiency Video Coding (HEVC) standard, intra prediction modes having the dependency are mode 2 to mode 9, mode 11 to mode 25, and mode 27 to mode 34 defined in the HEVC standard, and the second set of candidates is a subset including mode 0, mode 1, mode 10, and mode 26 defined in the HEV C standard.