Setting a foreign key to null when using entity framework code first

I'm using the database first implementation of Entity Framework Code First as the data layer for a project, but I've run into a problem.

I need to be able to set a foreign key to null in order to remove an association in the database.

I have 2 objects. One is called Project.

public class Project
{
    public int ProjectId {get; set;}
    public Employee Employee {get;set;}
}

public class Employee
{
    public int EmployeeId {get; set;}
    public string EmployeeName {get;set;}
}

This matches what I have in the Database:

CREATE TABLE Project(
    ProjectId int IDENTITY(1,1) NOT NULL,
    EmployeeId int NULL
)

CREATE TABLE Project(
    EmployeeId int IDENTITY(1,1) NOT NULL,
    EmployeeName varchar(100) NULL
)

I can assign an Employee to a project. However, I want to be able to remove an employee from a project and have the Employee field be null. In my UI this will show as 'No EMployee Assigned'.

However, short of a direct sql query, I cannot seem to find a way to do this in the entity framework 4.1.

I've tried:

public void RemoveEmployeeFromProject(int projectId)
{
    var project = Context.Projects.FirstOrDefault(x => x.ProjectId == projectId);
    project.Employee = null;
    Context.SaveChanges();
}

But this doesn't do anything.

Does anyone have any ideas?