We have developed a scaling theory for a salt-free solution of diblock polyampholytes. A charge-symmetric diblock polyampholyte chain with equally charged positive and negative blocks collapses into a globule. This collapse is driven by the electrostatic attraction between oppositely charged blocks. We predict that a charge-asymmetric block polyampholyte has a tadpole shape with a globular head and a polyelectrolyte tail. These tadpoles aggregate into micelles if the electrostatic repulsion between their tails is weaker than the surface energy gain due to aggregation of their heads. First tadpoles form double-tailed micelles. In double-tailed micelles with an aggregation number larger than two, additional chains are completely confined into the core, and the length of the two tails increases proportionally to the total charge of the micelle. If this total charge becomes higher than the charge of two corona blocks of double-tailed micelles, more blocks appear in the corona. Chains are disproportionated in all micelles. They are divided into two populations: chains in one group are completely confined inside the micellar core, while the other group of chains has an entire block placed in the corona. Micelles with disproportionated chains remain stable even if the net charge of a block polyampholyte is as small as one elementary charge per chain. This stability is due to (i) a long corona consisting of entire stronger charged blocks and (ii) weaker charged blocks in the core are not stretched because of the presence of entire diblock chains confined in the core.