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The Israeli government changed the dates of Yom HaZikaron and Yom Ha’atzmaut a couple of years ago. They added a new rule to prevent Yom HaZikaron from beginning on motzei Shabbat. In 2007, these holidays begin at sundown on 22 and 23 April, respectively (the 5th and 6th of Iyyar).

See Memorial Day and Independence Day Bill (amendment) 2004 for an English translation of the law that the Knesset passed.

The Wikipedia article on Yom Ha’atzmaut explains the recent change, and their dates agree with ours. Here the relevant excerpt:

Yom Ha’atzmaut falls on the 5th day of Iyar on the Hebrew calendar, the anniversary of the day in which Israel independence was proclaimed, when David ben Gurion publicly read the Proclamation of the establishment of the State of Israel. The corresponding Gregorian date was May 14, 1948.
The festival is celebrated on the Tuesday, Wednesday or Thursday closest to that date. This is to avoid having the festival either on Shabbat, the Jewish sabbath, or immediately before or after it. If Iyar 5 falls on Saturday, the festival is advanced to Thursday, Iyar 3, and if on Friday, then it is advanced to Thursday, Iyar 4. In 2004, the law was changed to provide that if Iyar 5 falls on Monday, the festival is postponed to Tuesday Iyar 6, so that Yom Hazikaron will not be immediately after the sabbath. (The rules of the Hebrew calendar are such that Iyar 5 does not fall on Sunday.)

If you’re using hebcal for UNIX, be sure to upgrade to version 3.7 to see the updated rules for these two holidays.