diff --git a/base/set.jl b/base/set.jl
index 1a25aa1c2a859..6afff54d7cf0a 100644
--- a/base/set.jl
+++ b/base/set.jl
@@ -178,16 +178,41 @@ function unique(f, C)
     out
 end
 
-# If A is not grouped, then we will need to keep track of all of the elements that we have
-# seen so far.
-function _unique!(A::AbstractVector)
-    seen = Set{eltype(A)}()
+"""
+    unique!(f, A::AbstractVector)
+
+Selects one value from `A` for each unique value produced by `f` applied to
+elements of `A` , then return the modified A.
+
+# Examples
+```jldoctest
+julia> unique!(x -> x^2, [1, -1, 3, -3, 4])
+3-element Array{Int64,1}:
+ 1
+ 3
+ 4
+
+julia> unique!(n -> n%3, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6])
+3-element Array{Int64,1}:
+ 5
+ 1
+ 9
+
+julia> unique!(iseven, [2, 3, 5, 7, 9])
+2-element Array{Int64,1}:
+ 2
+ 3
+```
+"""
+function unique!(f, A::AbstractVector)
+    seen = Set()
     idxs = eachindex(A)
     y = iterate(idxs)
     count = 0
     for x in A
-        if x ∉ seen
-            push!(seen, x)
+        t = f(x)
+        if t ∉ seen
+            push!(seen,t)
             count += 1
             A[y[1]] = x
             y = iterate(idxs, y[2])
@@ -196,6 +221,10 @@ function _unique!(A::AbstractVector)
     resize!(A, count)
 end
 
+# If A is not grouped, then we will need to keep track of all of the elements that we have
+# seen so far.
+_unique!(A::AbstractVector) = unique!(identity, A::AbstractVector)
+
 # If A is grouped, so that each unique element is in a contiguous group, then we only
 # need to keep track of one element at a time. We replace the elements of A with the
 # unique elements that we see in the order that we see them. Once we have iterated
diff --git a/test/sets.jl b/test/sets.jl
index e9342439f0a2f..ebe9db8ba90d9 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -398,6 +398,10 @@ end
     unique!(u)
     @test u == [5,"w","we","r"]
     u = [1,2,5,1,3,2]
+    @test unique!(x -> x ^ 2, [1, -1, 3, -3, 5, -5]) == [1, 3, 5]
+    @test unique!(n -> n % 3, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6]) == [5, 1, 9]
+    @test unique!(iseven, [2, 3, 5, 7, 9]) == [2, 3]
+    @test unique!(x -> x % 2 == 0 ? :even : :odd, [1, 2, 3, 4, 2, 2, 1]) == [1, 2]
 end
 
 @testset "allunique" begin