Does Java have a method to take a string with accented characters and
convert it to unaccented characters?  I want to search a big string for a
test string, ignoring accents on characters.

Doing the equivalent ignoring of case is simple:

String actualTestString = testString.toLowerCase();
String actualBigString = bigString.toLowerCase();
if (actualBigString.lastIndexOf(actualTestString) >= 0)
{
// do stuff
}

In the Collator class I see a way of checking if two strings are equivalent,
disregarding both case and accents:

Collator c = Collator.getInstance();
c.setStrength(Collator.PRIMARY);  // ignore both case and accents
if (c.compare(oneString, otherString) == 0)
{
//do stuff
}

However, I don't see a way of reducing the accented string to a simpler
string so I could search in a bigger string using a "toUnaccentedForm"
method instead of the toLowerCase method in the code above.

Is there a built-in method like "toUnaccentedForm" or some other approach
simpler than writing one's own version of lastIndexOf to ignore accents?