diff --git a/src/ol/render/webgl/Replay.js b/src/ol/render/webgl/Replay.js
index 4cd71cfce5..9a9adc2584 100644
--- a/src/ol/render/webgl/Replay.js
+++ b/src/ol/render/webgl/Replay.js
@@ -5,7 +5,7 @@ import {inherits} from '../../index.js';
 import {getCenter} from '../../extent.js';
 import _ol_render_VectorContext_ from '../VectorContext.js';
 import _ol_transform_ from '../../transform.js';
-import _ol_vec_Mat4_ from '../../vec/Mat4.js';
+import {create, fromTransform} from '../../vec/Mat4.js';
 import _ol_webgl_ from '../../webgl.js';
 
 /**
@@ -64,7 +64,7 @@ var _ol_render_webgl_Replay_ = function(tolerance, maxExtent) {
    * @private
    * @type {Array.<number>}
    */
-  this.tmpMat4_ = _ol_vec_Mat4_.create();
+  this.tmpMat4_ = create();
 
   /**
    * @protected
@@ -308,11 +308,11 @@ _ol_render_webgl_Replay_.prototype.replay = function(context,
   }
 
   gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, projectionMatrix));
+      fromTransform(this.tmpMat4_, projectionMatrix));
   gl.uniformMatrix4fv(locations.u_offsetScaleMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, offsetScaleMatrix));
+      fromTransform(this.tmpMat4_, offsetScaleMatrix));
   gl.uniformMatrix4fv(locations.u_offsetRotateMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, offsetRotateMatrix));
+      fromTransform(this.tmpMat4_, offsetRotateMatrix));
   gl.uniform1f(locations.u_opacity, opacity);
 
   // draw!
diff --git a/src/ol/renderer/webgl/Layer.js b/src/ol/renderer/webgl/Layer.js
index e92d04c9a4..2546e212fa 100644
--- a/src/ol/renderer/webgl/Layer.js
+++ b/src/ol/renderer/webgl/Layer.js
@@ -9,7 +9,7 @@ import _ol_renderer_Layer_ from '../Layer.js';
 import _ol_renderer_webgl_defaultmapshader_ from '../webgl/defaultmapshader.js';
 import _ol_renderer_webgl_defaultmapshader_Locations_ from '../webgl/defaultmapshader/Locations.js';
 import _ol_transform_ from '../../transform.js';
-import _ol_vec_Mat4_ from '../../vec/Mat4.js';
+import {create, fromTransform} from '../../vec/Mat4.js';
 import _ol_webgl_ from '../../webgl.js';
 import _ol_webgl_Buffer_ from '../../webgl/Buffer.js';
 import _ol_webgl_Context_ from '../../webgl/Context.js';
@@ -76,7 +76,7 @@ var _ol_renderer_webgl_Layer_ = function(mapRenderer, layer) {
    * @type {Array.<number>}
    * @private
    */
-  this.tmpMat4_ = _ol_vec_Mat4_.create();
+  this.tmpMat4_ = create();
 
   /**
    * @private
@@ -173,9 +173,9 @@ _ol_renderer_webgl_Layer_.prototype.composeFrame = function(frameState, layerSta
   }
 
   gl.uniformMatrix4fv(locations.u_texCoordMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, this.getTexCoordMatrix()));
+      fromTransform(this.tmpMat4_, this.getTexCoordMatrix()));
   gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
-      _ol_vec_Mat4_.fromTransform(this.tmpMat4_, this.getProjectionMatrix()));
+      fromTransform(this.tmpMat4_, this.getProjectionMatrix()));
   gl.uniform1f(locations.u_opacity, layerState.opacity);
   gl.bindTexture(_ol_webgl_.TEXTURE_2D, this.getTexture());
   gl.drawArrays(_ol_webgl_.TRIANGLE_STRIP, 0, 4);
diff --git a/src/ol/vec/Mat4.js b/src/ol/vec/Mat4.js
index dd662b3528..b3305bc0be 100644
--- a/src/ol/vec/Mat4.js
+++ b/src/ol/vec/Mat4.js
@@ -1,15 +1,14 @@
 /**
  * @module ol/vec/Mat4
  */
-var _ol_vec_Mat4_ = {};
 
 
 /**
  * @return {Array.<number>} 4x4 matrix representing a 3D identity transform.
  */
-_ol_vec_Mat4_.create = function() {
+export function create() {
   return [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];
-};
+}
 
 
 /**
@@ -17,7 +16,7 @@ _ol_vec_Mat4_.create = function() {
  * @param {ol.Transform} transform Transformation matrix.
  * @return {Array.<number>} 2D transformation matrix as flattened 4x4 matrix.
  */
-_ol_vec_Mat4_.fromTransform = function(mat4, transform) {
+export function fromTransform(mat4, transform) {
   mat4[0] = transform[0];
   mat4[1] = transform[1];
   mat4[4] = transform[2];
@@ -25,5 +24,4 @@ _ol_vec_Mat4_.fromTransform = function(mat4, transform) {
   mat4[12] = transform[4];
   mat4[13] = transform[5];
   return mat4;
-};
-export default _ol_vec_Mat4_;
+}
diff --git a/test/spec/ol/vec/mat4.test.js b/test/spec/ol/vec/mat4.test.js
index 7109131c5b..52b063d4e5 100644
--- a/test/spec/ol/vec/mat4.test.js
+++ b/test/spec/ol/vec/mat4.test.js
@@ -1,11 +1,11 @@
-import _ol_vec_Mat4_ from '../../../../src/ol/vec/Mat4.js';
+import {create, fromTransform} from '../../../../src/ol/vec/Mat4.js';
 
 
 describe('ol.vec.Mat4', function() {
 
   describe('ol.vec.Mat4.create()', function() {
     it('returns the expected matrix', function() {
-      expect(_ol_vec_Mat4_.create()).to.eql(
+      expect(create()).to.eql(
           [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]);
     });
   });
@@ -13,8 +13,8 @@ describe('ol.vec.Mat4', function() {
   describe('ol.vec.Mat4.fromTransform()', function() {
     it('sets the expected transform on the matrix', function() {
       var transform = [1, 2, 3, 4, 5, 6];
-      var result = _ol_vec_Mat4_.create();
-      expect(_ol_vec_Mat4_.fromTransform(result, transform)).to.eql(
+      var result = create();
+      expect(fromTransform(result, transform)).to.eql(
           [1, 2, 0, 0, 3, 4, 0, 0, 0, 0, 1, 0, 5, 6, 0, 1]);
       expect(result).to.eql(
           [1, 2, 0, 0, 3, 4, 0, 0, 0, 0, 1, 0, 5, 6, 0, 1]);