“YES IT IS” was the giant headline in The Standard, one of Kenya’s leading newspapers.

The new constitution is expected to be a crucial turning point in this country’s postcolonial history by finally addressing many of the political issues that have dogged this East African powerhouse since independence in 1963.

Voting began before dawn on Wednesday, and the high turnout had been expected because of the intense campaigning for and against the constitution over the past several months. But the vote was shadowed by memories of the disputed 2007 election, which set off ethnically fueled clashes across the country that left more than 1,000 people dead.

To prevent any sort of repeat, the Kenyan government overhauled the entire election process — not just registration, but also how the lines at polling stations would work and how ballot results would be transmitted — by cellphone and computer, — how votes would be tallied and how voters would be protected. Thousands of police officers have been sent to keep order in rural areas.

At the Baba Dogo primary school in Nairobi on Wednesday, calm prevailed. Beginning at 6 a.m., before the equatorial sun had cleared the horizon, voters gathered in orderly lines marked off by twine. No one was shouting, cheering or gloating about how they were going to vote. Street vendors had not preventively cleared out, as they often do during elections, fearing trouble, and instead were enjoying a brisk trade selling bananas, peanuts and Fantas to voters streaming out of the polls.

It was an atmosphere, people said, totally different from the election in 2007.

“It’s peaceful,” said Samson Omondi, a college student. “We’ve learned from last time.”

But the goal is far more than a clean vote without a violent aftermath. If the new constitution passes, it will curtail the powers of an imperial-style presidency, pave the way for much-needed land reform and give Kenyans a bill of rights, a combination that could spell the beginning of the end of one of the most corrupt, deeply entrenched political systems on the continent.

Of course, voting day itself in 2007 was not the problem. There were only a few flare-ups, but passions were running high — political supporters mobbed the polls, sporting the various colors of their parties. Tensions rose from there, and when a few days later the government appeared to have rigged the election to stay in power, fighting exploded. Many Kenyans said Wednesday they felt confident that this referendum was different enough and that even in the days ahead there would not be trouble. As of late Thursday morning, there had been no reports of violence as the word spread about the results, and no official challenges had been filed.

“The big forces have come in on one side,” explained Joash Mbulika, a human resources manager at a manufacturing plant in the Baba Dogo area. He was referring to the fact that Kenya’s top leaders — the president, the prime minister, the vice president, the deputy prime ministers and many other “samaki kubwa,” or “big fish” in Swahili — were all pushing for the new constitution. Last time around, they were struggling with one another for power.

The one part of the country that could be the exception is the Rift Valley, Kenya’s breadbasket and also the epicenter of the ethnic violence two and a half years ago. The Rift Valley is dominated by the Kalenjin ethnic group, which has largely been supporting the “no” campaign, partially because of concerns over land reform.

But on Wednesday, officials in ethnically mixed Rift Valley areas that had been flashpoints in 2007 said there were no problems so far.

“Things are going smoothly,” said Chief Nahason Jason Mwaniki. “There’s lot of security.”

Pre-referendum polls showed the new constitution getting at least 60 percent approval (it needed a simple majority and 25 percent of the votes in five of Kenya’s eight provinces). Most voters interviewed in Nairobi on Wednesday said they had scratched their X next to the green “yes” box.

“We’ve had a dictatorship-kind of leadership since independence,” Oliver Ochieng, a high school teacher, said Wednesday. “We need to change.”

The early referendum results showed that political leaders still held enormous sway over their ethnic communities, an influence that many observers said was exploited during the 2007 election and stoked the violence.

On Wednesday, in some polling places in strongholds of leaders who were supporting the constitution, the “yes” votes were leading by more than 99 percent. The mirror image was true in strongholds of the politicians who had been opposing the constitution. In their areas, upwards of 90 percent of the people had voted “no.