Eliminate duplicates of nonzero elements but keep zeros

 I have a logical array. I want to eliminate the duplicates of the 1s but keep all the zeros intact. 
Here's an example of what I want.
A = [0 1 0 1 1 0 0 0 0 0 1 1 1 0 1]
new matrix = [0 1 0 1 0 0 0 0 0 1 0 1].
The zeros are the same but all the duplicate 1s after the first are eliminated.

Answer 1

[Azzi Abdelmalek]

A = [0 1 0 1 1 0 0 0 0 0 1 1 1 0 1]
A(strfind(A,[1,1]))=[]

[Alice]

Hi Azzi, I'd like to put it into another matrix. How do I go about doing that? Thank you for the answer.

[Azzi Abdelmalek]

A = [0 1 0 1 1 0 0 0 0 0 1 1 1 0 1];
B=A;
B(strfind(B,[1,1]))=[]

Answer 2

[Andrei Bobrov]

A(~([false,diff(A)] == 0 & A == 1))