There exists a unique perpetual (solar) calendar with leap week that could become the basis for an eventual world calendar reform. Unlike the Universal Calendar considered for such a reform by the UN in 1956, rejected in a vote, it does not interrupt the continuity of weeks, which was the chief objection against this calendar. Except for the mentioned serious chronological defect, the Universal Calendar would otherwise have had many advantages. The leap week concept had been suggested earlier, but was never elaborated properly. Relevant theoretical questions and a suitable form of the calendar based on this concept are discussed. There is also a glimpse of the possible form of our calendar in a very distant future and of a calendar in cosmic space. The new calendar proposed is an optimum compromise for a solar calendar. While preserving advantages of the Universal Calendar, it fulfills all modern requirements: constancy, uniformity, continuity, simplicity and accuracy. With the leap rule derived (with regard to uniform time) an error of one day would occur in the new calendar in an interval longer than 10000 years. It could obtain a global acceptance, because there would be no discordance in the day of the week with respect to other existing calendars having a weekly cycle (such as, e.g., Jewish, Muslim, etc.).