Using private static nested class to implement Singleton

I am currently learning about the Singleton pattern. I learnt that the classic way to implement it is to create a static field of the Singleton class type, hide the constructor using private access modifier, and provide a public getInstance() method.

However, I thought of another way of implementing it without using private constructors:

public class SWrapper {
    private static Singleton holder = new Singleton();
    private static class Singleton{ /* implementation without private constructor*/}
    public static Singleton getInstance() {
        return holder;
}

QUESTION: Does this implementation work? (I think it does but I can't be sure.) If it does, are there any advantages or disadvantages to using this implementation?