Static constructor - Singleton Design pattern in c#

What if, I replaced private constructor with a static constructor in singleton Design pattern?

public sealed class Singleton
{
    private static Singleton instance=null;

    private Singleton()
    {
    }

    public static Singleton Instance
    {
        get
        {
            if (instance==null)
            {
                instance = new Singleton();
            }
            return instance;
        }
    }
}

Static constructor will be called only once and I couldn't find any difference in the implementation. Can we replace private with static constructor?